Examples

[\begin{matrix} 4 & - 3 0 & 1 \end{matrix}] - [\begin{matrix} 4 & - 1 - 12 & - 2 \end{matrix}]

$[\begin{array}{c} 4 & - 3 \\ 0 & 1 \end{array}] - [\begin{array}{c} 4 & - 1 \\ - 12 & - 2 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 4 - 4 & - 3 + 1 \\ 0 + 12 & 1 + 2 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract

$4$ from

$4$ .

$[\begin{array}{c} 0 & - 3 + 1 \\ 0 + 12 & 1 + 2 \end{array}]$

Step 2.2

Add

$- 3$ and

$1$ .

$[\begin{array}{c} 0 & - 2 \\ 0 + 12 & 1 + 2 \end{array}]$

Step 2.3

Add

$0$ and

$12$ .

$[\begin{array}{c} 0 & - 2 \\ 12 & 1 + 2 \end{array}]$

Step 2.4

Add

$1$ and

$2$ .

$[\begin{array}{c} 0 & - 2 \\ 12 & 3 \end{array}]$

Step 3

The determinant of a

$2 \times 2$ matrix can be found using the formula

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$0 \cdot 3 - 12 \cdot - 2$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply

$0$ by

$3$ .

$0 - 12 \cdot - 2$

Step 4.1.2

Multiply

$- 12$ by

$- 2$ .

$0 + 24$

Step 4.2

Add

$0$ and

$24$ .

$24$

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