Aljabar Linear Contoh

$[\begin{array}{c} - \frac{1}{\sqrt{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2

Gabungkan dan sederhanakan penyebutnya.

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Langkah 2.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.6.4

Batalkan faktor persekutuan dari $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.6.4.1

Batalkan faktor persekutuan.

Langkah 2.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 2.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 3

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4

Gabungkan dan sederhanakan penyebutnya.

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.6.4

Batalkan faktor persekutuan dari $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.6.4.1

Batalkan faktor persekutuan.

Langkah 4.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 4.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 5

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6

Gabungkan dan sederhanakan penyebutnya.

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.2

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.3

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.6

Tulis kembali ${\sqrt{3}}^{2}$ sebagai $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 6.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{3}$ sebagai $3^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 6.6.4.1

Batalkan faktor persekutuan.

Langkah 6.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{1}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 6.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 7

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8

Gabungkan dan sederhanakan penyebutnya.

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Langkah 8.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

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Langkah 8.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 8.6.4.1

Batalkan faktor persekutuan.

Langkah 8.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{1}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 8.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 9

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10

Gabungkan dan sederhanakan penyebutnya.

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Langkah 10.1

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.2

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.3

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.6

Tulis kembali ${\sqrt{3}}^{2}$ sebagai $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 10.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{3}$ sebagai $3^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.6.4

Batalkan faktor persekutuan dari $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 10.6.4.1

Batalkan faktor persekutuan.

Langkah 10.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3^{1}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 10.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 11

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12

Gabungkan dan sederhanakan penyebutnya.

Ketuk untuk lebih banyak langkah...

Langkah 12.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 12.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 12.6.4.1

Batalkan faktor persekutuan.

Langkah 12.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 12.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 13

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14

Gabungkan dan sederhanakan penyebutnya.

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Langkah 14.1

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.2

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.3

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.6

Tulis kembali ${\sqrt{3}}^{2}$ sebagai $3$ .

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Langkah 14.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{3}$ sebagai $3^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 14.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 14.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 15

Kalikan $[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}]$ .

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Langkah 15.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $3 \times 3$ and the second matrix is $3 \times 3$ .

Langkah 15.2

Kalikan setiap baris pada matriks pertama dengan setiap kolom pada matriks kedua.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} \cdot 1 - \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{2}}{2} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ \frac{\sqrt{2}}{2} \cdot 1 + 0 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 + 0 \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 + 0 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ 0 \cdot 1 + \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + \frac{\sqrt{2}}{2} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 15.3

Sederhanakan setiap elemen dalam matriks dengan mengalikan semua pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 16

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17

Gabungkan dan sederhanakan penyebutnya.

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Langkah 17.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

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Langkah 17.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 17.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 17.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 18

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19

Gabungkan dan sederhanakan penyebutnya.

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Langkah 19.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

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Langkah 19.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 19.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{1}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 19.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 20

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21

Gabungkan dan sederhanakan penyebutnya.

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Langkah 21.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

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Langkah 21.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 21.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{1}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 21.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 22

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23

Gabungkan dan sederhanakan penyebutnya.

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Langkah 23.1

Kalikan $\frac{1}{\sqrt{2}}$ dengan $\frac{\sqrt{2}}{\sqrt{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.2

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.3

Naikkan $\sqrt{2}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.6

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 23.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 23.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 23.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 24

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25

Gabungkan dan sederhanakan penyebutnya.

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Langkah 25.1

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.2

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.3

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.6

Tulis kembali ${\sqrt{3}}^{2}$ sebagai $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 25.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{3}$ sebagai $3^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 25.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 25.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 26

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27

Gabungkan dan sederhanakan penyebutnya.

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Langkah 27.1

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.2

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.3

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.6

Tulis kembali ${\sqrt{3}}^{2}$ sebagai $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 27.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{3}$ sebagai $3^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.6.4

Batalkan faktor persekutuan dari $2$ .

Ketuk untuk lebih banyak langkah...

Langkah 27.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 27.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \end{array}]$

Langkah 28

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}]$

Langkah 29

Gabungkan dan sederhanakan penyebutnya.

Ketuk untuk lebih banyak langkah...

Langkah 29.1

Kalikan $\frac{1}{\sqrt{3}}$ dengan $\frac{\sqrt{3}}{\sqrt{3}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}]$

Langkah 29.2

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}]$

Langkah 29.3

Naikkan $\sqrt{3}$ menjadi pangkat $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}]$

Langkah 29.4

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}]$

Langkah 29.5

Tambahkan $1$ dan $1$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}]$

Langkah 29.6

Tulis kembali ${\sqrt{3}}^{2}$ sebagai $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 29.6.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{3}$ sebagai $3^{\frac{1}{2}}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}]$

Langkah 29.6.2

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}]$

Langkah 29.6.3

Gabungkan $\frac{1}{2}$ dan $2$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

Langkah 29.6.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 29.6.4.1

Batalkan faktor persekutuan.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

Langkah 29.6.4.2

Tulis kembali pernyataannya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} \end{array}]$

Langkah 29.6.5

Evaluasi eksponennya.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$

Langkah 30

Kalikan $[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$ .

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Langkah 30.1

Langkah 30.2

Kalikan setiap baris pada matriks pertama dengan setiap kolom pada matriks kedua.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) - \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2} \cdot 0 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) + 0 (- \frac{\sqrt{2}}{2}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} + 0 \cdot 0 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot 0 + 0 \frac{\sqrt{2}}{2} + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ 0 (- \frac{\sqrt{2}}{2}) + \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} \cdot 0 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \cdot 0 + \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \end{array}]$

Langkah 30.3

Sederhanakan setiap elemen dalam matriks dengan mengalikan semua pernyataannya.

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Langkah 30.3.1

Kalikan $4$ dengan $2$ .

$[\begin{array}{c} \frac{7}{3} & \frac{5}{6} & \frac{5}{6} \\ \frac{5}{6} & \frac{11}{6} & \frac{4}{3} \\ \frac{5}{6} & \frac{4}{3} & \frac{3 + 8}{6} \end{array}]$

Langkah 30.3.2

Tambahkan $3$ dan $8$ .

$[\begin{array}{c} \frac{7}{3} & \frac{5}{6} & \frac{5}{6} \\ \frac{5}{6} & \frac{11}{6} & \frac{4}{3} \\ \frac{5}{6} & \frac{4}{3} & \frac{11}{6} \end{array}]$