Find Pivot Positions and Pivot Columns [[12],[11],[4]]

$[\begin{array}{c} 12 \\ 11 \\ 4 \end{array}]$

Step 1

Find the reduced row echelon form.

Multiply each element of $R_{1}$ by $\frac{1}{12}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{12}{12} \\ 11 \\ 4 \end{array}]$

Simplify $R_{1}$ .

$[\begin{array}{c} 1 \\ 11 \\ 4 \end{array}]$

Perform the row operation $R_{2} = R_{2} - 11 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 \\ 11 - 11 \cdot 1 \\ 4 \end{array}]$

Simplify $R_{2}$ .

$[\begin{array}{c} 1 \\ 0 \\ 4 \end{array}]$

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 \\ 0 \\ 4 - 4 \cdot 1 \end{array}]$

Simplify $R_{3}$ .

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

Step 2

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: $a_{11}$

Pivot Columns: $1$