Linear Algebra Examples

$[\begin{array}{c} 1 & 0 & \frac{2}{9} \\ 0 & 1 & - \frac{4}{9} \\ 0 & 0 & 0 \end{array}]$

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: $a_{11}$ and $a_{22}$

Pivot Columns: $1$ and $2$

Step 2

The rank is the number of pivot columns.

$2$