Precalculus Examples

$[\begin{array}{c} 2 & 1 \\ 4 & 1 \end{array}] - [\begin{array}{c} - 3 & - 3 \\ - 5 & - 3 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 2 + 3 & 1 + 3 \\ 4 + 5 & 1 + 3 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $2$ and $3$ .

$[\begin{array}{c} 5 & 1 + 3 \\ 4 + 5 & 1 + 3 \end{array}]$

Step 2.2

Add $1$ and $3$ .

$[\begin{array}{c} 5 & 4 \\ 4 + 5 & 1 + 3 \end{array}]$

Step 2.3

Add $4$ and $5$ .

$[\begin{array}{c} 5 & 4 \\ 9 & 1 + 3 \end{array}]$

Step 2.4

Add $1$ and $3$ .

$[\begin{array}{c} 5 & 4 \\ 9 & 4 \end{array}]$

Step 3

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

$5 \cdot 4 - 9 \cdot 4$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $5$ by $4$ .

$20 - 9 \cdot 4$

Step 4.1.2

Multiply $- 9$ by $4$ .

$20 - 36$

Step 4.2

Subtract $36$ from $20$ .

$- 16$

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