Linear Algebra Examples

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

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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