Linear Algebra Examples

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

Step 1

Add the corresponding elements.

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

Step 2

Simplify each element.

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Step 2.1

Add $2$ and $4$ .

$[\begin{array}{c} 6 & 4 - 1 \\ - 2 + 3 & - 4 + 2 \end{array}]$

Step 2.2

Subtract $1$ from $4$ .

$[\begin{array}{c} 6 & 3 \\ - 2 + 3 & - 4 + 2 \end{array}]$

Step 2.3

Add $- 2$ and $3$ .

$[\begin{array}{c} 6 & 3 \\ 1 & - 4 + 2 \end{array}]$

Step 2.4

Add $- 4$ and $2$ .

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

Step 3

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

$6 \cdot - 2 - 1 \cdot 3$

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 $- 2$ .

$- 12 - 1 \cdot 3$

Step 4.1.2

Multiply $- 1$ by $3$ .

$- 12 - 3$

Step 4.2

Subtract $3$ from $- 12$ .

$- 15$

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