Linear Algebra Examples

$[\begin{array}{c} 2 & 4 \\ 6 & 8 \end{array}] - [\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 2 - 1 & 4 - 2 \\ 6 - 3 & 8 - 4 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $1$ from $2$ .

$[\begin{array}{c} 1 & 4 - 2 \\ 6 - 3 & 8 - 4 \end{array}]$

Step 2.2

Subtract $2$ from $4$ .

$[\begin{array}{c} 1 & 2 \\ 6 - 3 & 8 - 4 \end{array}]$

Step 2.3

Subtract $3$ from $6$ .

$[\begin{array}{c} 1 & 2 \\ 3 & 8 - 4 \end{array}]$

Step 2.4

Subtract $4$ from $8$ .

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

Step 3

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

$1 \cdot 4 - 3 \cdot 2$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $4$ by $1$ .

$4 - 3 \cdot 2$

Step 4.1.2

Multiply $- 3$ by $2$ .

$4 - 6$

Step 4.2

Subtract $6$ from $4$ .

$- 2$

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