Linear Algebra Examples

$[\begin{array}{c} 7 & 2 \\ 1 & 3 \end{array}] - [\begin{array}{c} 1 & 2 \\ 5 & 6 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 7 - 1 & 2 - 2 \\ 1 - 5 & 3 - 6 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $1$ from $7$ .

$[\begin{array}{c} 6 & 2 - 2 \\ 1 - 5 & 3 - 6 \end{array}]$

Step 2.2

Subtract $2$ from $2$ .

$[\begin{array}{c} 6 & 0 \\ 1 - 5 & 3 - 6 \end{array}]$

Step 2.3

Subtract $5$ from $1$ .

$[\begin{array}{c} 6 & 0 \\ - 4 & 3 - 6 \end{array}]$

Step 2.4

Subtract $6$ from $3$ .

$[\begin{array}{c} 6 & 0 \\ - 4 & - 3 \end{array}]$

Step 3

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

$6 \cdot - 3 - (- 4 \cdot 0)$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $6$ by $- 3$ .

$- 18 - (- 4 \cdot 0)$

Step 4.1.2

Multiply $- (- 4 \cdot 0)$ .

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Step 4.1.2.1

Multiply $- 4$ by $0$ .

$- 18 - 0$

Step 4.1.2.2

Multiply $- 1$ by $0$ .

$- 18 + 0$

Step 4.2

Add $- 18$ and $0$ .

$- 18$