Algebra Examples

$[\begin{array}{c} 6 & 7 \\ 9 & 7 \end{array}]$

Step 1

Find the reduced row echelon form.

Tap for more steps...

Step 1.1

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

Tap for more steps...

Step 1.1.1

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{6}{6} & \frac{7}{6} \\ 9 & 7 \end{array}]$

Step 1.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & \frac{7}{6} \\ 9 & 7 \end{array}]$

Step 1.2

Perform the row operation $R_{2} = R_{2} - 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

Tap for more steps...

Step 1.2.1

Perform the row operation $R_{2} = R_{2} - 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{7}{6} \\ 9 - 9 \cdot 1 & 7 - 9 (\frac{7}{6}) \end{array}]$

Step 1.2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{7}{6} \\ 0 & - \frac{7}{2} \end{array}]$

Step 1.3

Multiply each element of $R_{2}$ by $- \frac{2}{7}$ to make the entry at $2, 2$ a $1$ .

Tap for more steps...

Step 1.3.1

Multiply each element of $R_{2}$ by $- \frac{2}{7}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{7}{6} \\ - \frac{2}{7} \cdot 0 & - \frac{2}{7} (- \frac{7}{2}) \end{array}]$

Step 1.3.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & \frac{7}{6} \\ 0 & 1 \end{array}]$

Step 1.4

Perform the row operation $R_{1} = R_{1} - \frac{7}{6} R_{2}$ to make the entry at $1, 2$ a $0$ .

Tap for more steps...

Step 1.4.1

Perform the row operation $R_{1} = R_{1} - \frac{7}{6} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{7}{6} \cdot 0 & \frac{7}{6} - \frac{7}{6} \cdot 1 \\ 0 & 1 \end{array}]$

Step 1.4.2

Simplify $R_{1}$ .

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

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

Pivot Columns: $1$ and $2$

Step 3

The rank is the number of pivot columns.

$2$

Enter YOUR Problem