Find the Inverse [[17,21],[21,26]]

$[\begin{array}{c} 17 & 21 \\ 21 & 26 \end{array}]$

Step 1

The inverse of a $2 \times 2$ matrix can be found using the formula $\frac{1}{a d - b c} [\begin{array}{c} d & - b \\ - c & a \end{array}]$ where $a d - b c$ is the determinant.

Step 2

Find the determinant.

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$17 \cdot 26 - 21 \cdot 21$

Simplify the determinant.

Simplify each term.

Multiply $17$ by $26$ .

$442 - 21 \cdot 21$

Multiply $- 21$ by $21$ .

$442 - 441$

Subtract $441$ from $442$ .

$1$

Step 3

Substitute the known values into the formula for the inverse.

$\frac{1}{1} [\begin{array}{c} 26 & - 21 \\ - 21 & 17 \end{array}]$

Step 4

Divide $1$ by $1$ .

$1 [\begin{array}{c} 26 & - 21 \\ - 21 & 17 \end{array}]$

Step 5

Multiply $1$ by each element of the matrix.

$[\begin{array}{c} 1 \cdot 26 & 1 \cdot - 21 \\ 1 \cdot - 21 & 1 \cdot 17 \end{array}]$

Step 6

Simplify each element in the matrix.

Multiply $26$ by $1$ .

$[\begin{array}{c} 26 & 1 \cdot - 21 \\ 1 \cdot - 21 & 1 \cdot 17 \end{array}]$

Multiply $- 21$ by $1$ .

$[\begin{array}{c} 26 & - 21 \\ 1 \cdot - 21 & 1 \cdot 17 \end{array}]$

Multiply $- 21$ by $1$ .

$[\begin{array}{c} 26 & - 21 \\ - 21 & 1 \cdot 17 \end{array}]$

Multiply $17$ by $1$ .

$[\begin{array}{c} 26 & - 21 \\ - 21 & 17 \end{array}]$

Find the Inverse [[17,21],[21,26]]

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