Linear Algebra Examples

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

Step 1

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

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

Step 2

Simplify $R_{3}$ .

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