Linear Algebra Examples

$[\begin{array}{c} 1 & 3 & 6 \\ 1 & 4 & 5 \end{array}]$

Step 1

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

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Step 1.1

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

$[\begin{array}{c} 1 & 3 & 6 \\ 1 - 1 & 4 - 3 & 5 - 6 \end{array}]$

Step 1.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 3 & 6 \\ 0 & 1 & - 1 \end{array}]$

Step 2

Perform the row operation $R_{1} = R_{1} - 3 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Step 2.1

Perform the row operation $R_{1} = R_{1} - 3 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 3 \cdot 0 & 3 - 3 \cdot 1 & 6 - 3 \cdot - 1 \\ 0 & 1 & - 1 \end{array}]$

Step 2.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 9 \\ 0 & 1 & - 1 \end{array}]$