Examples

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

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

Step 1

Subtract the corresponding elements.

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

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

Step 2

Simplify each element.

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Step 2.1

Add

2

$2$ and

3

$3$ .

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

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

Step 2.2

Add

1

$1$ and

3

$3$ .

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

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

Step 2.3

Add

4

$4$ and

5

$5$ .

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

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

Step 2.4

Add

1

$1$ and

3

$3$ .

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

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

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

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

Step 3

The determinant of a

2 \times 2

$2 \times 2$ matrix can be found using the formula

| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

5 \cdot 4 - 9 \cdot 4

$5 \cdot 4 - 9 \cdot 4$

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

$5$ by

4

$4$ .

20 - 9 \cdot 4

$20 - 9 \cdot 4$

Step 4.1.2

Multiply

- 9

$- 9$ by

4

$4$ .

20 - 36

$20 - 36$

20 - 36

$20 - 36$

Step 4.2

Subtract

36

$36$ from

20

$20$ .

- 16

$- 16$

- 16

$- 16$

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