Álgebra lineal Ejemplos

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

Paso 1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 2

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 2.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 2.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 2.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 2.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 2.5

Suma $1$ y $1$ .

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

Paso 2.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 2.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 2.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 2.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 2.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 2.6.4.1

Cancela el factor común.

Paso 2.6.4.2

Reescribe la expresión.

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

Paso 2.6.5

Evalúa el exponente.

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

Paso 3

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 4

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 4.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 4.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 4.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 4.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 4.5

Suma $1$ y $1$ .

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

Paso 4.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 4.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 4.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 4.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 4.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 4.6.4.1

Cancela el factor común.

Paso 4.6.4.2

Reescribe la expresión.

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

Paso 4.6.5

Evalúa el exponente.

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

Paso 5

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 6

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 6.1

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 6.2

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 6.3

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 6.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 6.5

Suma $1$ y $1$ .

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

Paso 6.6

Reescribe ${\sqrt{3}}^{2}$ como $3$ .

Toca para ver más pasos...

Paso 6.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{3}$ como $3^{\frac{1}{2}}$ .

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

Paso 6.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 6.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 6.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 6.6.4.1

Cancela el factor común.

Paso 6.6.4.2

Reescribe la expresión.

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

Paso 6.6.5

Evalúa el exponente.

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

Paso 7

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 8

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 8.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 8.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 8.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 8.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 8.5

Suma $1$ y $1$ .

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

Paso 8.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 8.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 8.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 8.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 8.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 8.6.4.1

Cancela el factor común.

Paso 8.6.4.2

Reescribe la expresión.

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

Paso 8.6.5

Evalúa el exponente.

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

Paso 9

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 10

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 10.1

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 10.2

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 10.3

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 10.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 10.5

Suma $1$ y $1$ .

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

Paso 10.6

Reescribe ${\sqrt{3}}^{2}$ como $3$ .

Toca para ver más pasos...

Paso 10.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{3}$ como $3^{\frac{1}{2}}$ .

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

Paso 10.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 10.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 10.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 10.6.4.1

Cancela el factor común.

Paso 10.6.4.2

Reescribe la expresión.

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

Paso 10.6.5

Evalúa el exponente.

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

Paso 11

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 12

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 12.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 12.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 12.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 12.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 12.5

Suma $1$ y $1$ .

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

Paso 12.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 12.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 12.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 12.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 12.6.4

Cancela el factor común de $2$ .

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Paso 12.6.4.1

Cancela el factor común.

Paso 12.6.4.2

Reescribe la expresión.

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

Paso 12.6.5

Evalúa el exponente.

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

Paso 13

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 14

Combina y simplifica el denominador.

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Paso 14.1

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 14.2

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 14.3

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 14.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 14.5

Suma $1$ y $1$ .

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

Paso 14.6

Reescribe ${\sqrt{3}}^{2}$ como $3$ .

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Paso 14.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{3}$ como $3^{\frac{1}{2}}$ .

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

Paso 14.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 14.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 14.6.4

Cancela el factor común de $2$ .

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Paso 14.6.4.1

Cancela el factor común.

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

Paso 14.6.4.2

Reescribe la expresión.

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

Paso 14.6.5

Evalúa el exponente.

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

Paso 15

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

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Paso 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 $3 \times 3$ .

Paso 15.2

Multiplica cada fila en la primera matriz por cada columna en la segunda matriz.

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

Paso 15.3

Simplifica cada elemento de la matriz mediante la multiplicación de todas las expresiones.

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

Paso 16

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 17

Combina y simplifica el denominador.

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Paso 17.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 17.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 17.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 17.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 17.5

Suma $1$ y $1$ .

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

Paso 17.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

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Paso 17.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 17.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 17.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 17.6.4

Cancela el factor común de $2$ .

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Paso 17.6.4.1

Cancela el factor común.

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

Paso 17.6.4.2

Reescribe la expresión.

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

Paso 17.6.5

Evalúa el exponente.

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

Paso 18

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 19

Combina y simplifica el denominador.

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Paso 19.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 19.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 19.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 19.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 19.5

Suma $1$ y $1$ .

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

Paso 19.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 19.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 19.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 19.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 19.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 19.6.4.1

Cancela el factor común.

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

Paso 19.6.4.2

Reescribe la expresión.

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

Paso 19.6.5

Evalúa el exponente.

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

Paso 20

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 21

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 21.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 21.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 21.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 21.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 21.5

Suma $1$ y $1$ .

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

Paso 21.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 21.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 21.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 21.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 21.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 21.6.4.1

Cancela el factor común.

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

Paso 21.6.4.2

Reescribe la expresión.

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

Paso 21.6.5

Evalúa el exponente.

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

Paso 22

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 23

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 23.1

Multiplica $\frac{1}{\sqrt{2}}$ por $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Paso 23.2

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 23.3

Eleva $\sqrt{2}$ a la potencia de $1$ .

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

Paso 23.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 23.5

Suma $1$ y $1$ .

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

Paso 23.6

Reescribe ${\sqrt{2}}^{2}$ como $2$ .

Toca para ver más pasos...

Paso 23.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{2}$ como $2^{\frac{1}{2}}$ .

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

Paso 23.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 23.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 23.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 23.6.4.1

Cancela el factor común.

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

Paso 23.6.4.2

Reescribe la expresión.

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

Paso 23.6.5

Evalúa el exponente.

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

Paso 24

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 25

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 25.1

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 25.2

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 25.3

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 25.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 25.5

Suma $1$ y $1$ .

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

Paso 25.6

Reescribe ${\sqrt{3}}^{2}$ como $3$ .

Toca para ver más pasos...

Paso 25.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{3}$ como $3^{\frac{1}{2}}$ .

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

Paso 25.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 25.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 25.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 25.6.4.1

Cancela el factor común.

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

Paso 25.6.4.2

Reescribe la expresión.

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

Paso 25.6.5

Evalúa el exponente.

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

Paso 26

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 27

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 27.1

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 27.2

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 27.3

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 27.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 27.5

Suma $1$ y $1$ .

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

Paso 27.6

Reescribe ${\sqrt{3}}^{2}$ como $3$ .

Toca para ver más pasos...

Paso 27.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{3}$ como $3^{\frac{1}{2}}$ .

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

Paso 27.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 27.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 27.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 27.6.4.1

Cancela el factor común.

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

Paso 27.6.4.2

Reescribe la expresión.

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

Paso 27.6.5

Evalúa el exponente.

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

Paso 28

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 29

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 29.1

Multiplica $\frac{1}{\sqrt{3}}$ por $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Paso 29.2

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 29.3

Eleva $\sqrt{3}$ a la potencia de $1$ .

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

Paso 29.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 29.5

Suma $1$ y $1$ .

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

Paso 29.6

Reescribe ${\sqrt{3}}^{2}$ como $3$ .

Toca para ver más pasos...

Paso 29.6.1

Usa $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescribir $\sqrt{3}$ como $3^{\frac{1}{2}}$ .

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

Paso 29.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 29.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 29.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 29.6.4.1

Cancela el factor común.

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

Paso 29.6.4.2

Reescribe la expresión.

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

Paso 29.6.5

Evalúa el exponente.

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

Paso 30

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

Toca para ver más pasos...

Paso 30.1

Paso 30.2

Multiplica cada fila en la primera matriz por cada columna en la segunda matriz.

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

Paso 30.3

Simplifica cada elemento de la matriz mediante la multiplicación de todas las expresiones.

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Paso 30.3.1

Multiplica $4$ por $2$ .

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

Paso 30.3.2

Suma $3$ y $8$ .

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