Linear Algebra Examples

$[\begin{array}{c} 1 & 7 & 0 \\ 0 & 1 & 8 \\ 0 & 0 & 1 \end{array}]$

Step 1

Perform the row operation $R_{2} = R_{2} - 8 R_{3}$ to make the entry at $2, 3$ a $0$ .

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Step 1.1

Perform the row operation $R_{2} = R_{2} - 8 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 7 & 0 \\ 0 - 8 \cdot 0 & 1 - 8 \cdot 0 & 8 - 8 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

Step 1.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 7 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Step 2

Perform the row operation $R_{1} = R_{1} - 7 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Step 2.1

Perform the row operation $R_{1} = R_{1} - 7 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 7 \cdot 0 & 7 - 7 \cdot 1 & 0 - 7 \cdot 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Step 2.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$