Linear Algebra Examples

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

Step 1

The pivot positions are the locations with the leading $1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions: $a_{11}, a_{23},$ and $a_{36}$

Pivot Columns: $1, 3,$ and $6$