Matematika Berhingga Contoh

$[\begin{array}{c} 0.7 & - 0.3 & 1 & 0 \\ - 0.35 & 0.6 & 0 & 1 \end{array}]$

Langkah 1

Multiply each element of $R_{1}$ by $\frac{1}{0.7}$ to make the entry at $1, 1$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 1.1

Multiply each element of $R_{1}$ by $\frac{1}{0.7}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.7}{0.7} & \frac{- 0.3}{0.7} & \frac{1}{0.7} & \frac{0}{0.7} \\ - 0.35 & 0.6 & 0 & 1 \end{array}]$

Langkah 1.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & - 0.\overline{428571} & 1.\overline{428571} & 0 \\ - 0.35 & 0.6 & 0 & 1 \end{array}]$

Langkah 2

Perform the row operation $R_{2} = R_{2} + 0.35 R_{1}$ to make the entry at $2, 1$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Perform the row operation $R_{2} = R_{2} + 0.35 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - 0.\overline{428571} & 1.\overline{428571} & 0 \\ - 0.35 + 0.35 \cdot 1 & 0.6 + 0.35 \cdot - 0.\overline{428571} & 0 + 0.35 \cdot 1.\overline{428571} & 1 + 0.35 \cdot 0 \end{array}]$

Langkah 2.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & - 0.\overline{428571} & 1.\overline{428571} & 0 \\ 0 & 0.45 & 0.5 & 1 \end{array}]$

Langkah 3

Multiply each element of $R_{2}$ by $\frac{1}{0.45}$ to make the entry at $2, 2$ a $1$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.1

Multiply each element of $R_{2}$ by $\frac{1}{0.45}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 0.\overline{428571} & 1.\overline{428571} & 0 \\ \frac{0}{0.45} & \frac{0.45}{0.45} & \frac{0.5}{0.45} & \frac{1}{0.45} \end{array}]$

Langkah 3.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & - 0.\overline{428571} & 1.\overline{428571} & 0 \\ 0 & 1 & 1.\overline{1} & 2.\overline{2} \end{array}]$

Langkah 4

Perform the row operation $R_{1} = R_{1} + 0.\overline{428571} R_{2}$ to make the entry at $1, 2$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Perform the row operation $R_{1} = R_{1} + 0.\overline{428571} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + 0.\overline{428571} \cdot 0 & - 0.\overline{428571} + 0.\overline{428571} \cdot 1 & 1.\overline{428571} + 0.\overline{428571} \cdot 1.\overline{1} & 0 + 0.\overline{428571} \cdot 2.\overline{2} \\ 0 & 1 & 1.\overline{1} & 2.\overline{2} \end{array}]$

Langkah 4.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 1.\overline{904761} & 0.\overline{952380} \\ 0 & 1 & 1.\overline{1} & 2.\overline{2} \end{array}]$