Finite Math Examples

$1 [\begin{array}{c} 5 & 0 \\ 4 & - 3 \end{array}]$

Step 1

Multiply $1$ by each element of the matrix.

$[\begin{array}{c} 1 \cdot 5 & 1 \cdot 0 \\ 1 \cdot 4 & 1 \cdot - 3 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $5$ by $1$ .

$[\begin{array}{c} 5 & 1 \cdot 0 \\ 1 \cdot 4 & 1 \cdot - 3 \end{array}]$

Step 2.2

Multiply $0$ by $1$ .

$[\begin{array}{c} 5 & 0 \\ 1 \cdot 4 & 1 \cdot - 3 \end{array}]$

Step 2.3

Multiply $4$ by $1$ .

$[\begin{array}{c} 5 & 0 \\ 4 & 1 \cdot - 3 \end{array}]$

Step 2.4

Multiply $- 3$ by $1$ .

$[\begin{array}{c} 5 & 0 \\ 4 & - 3 \end{array}]$

Step 3

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

$5 \cdot - 3 - 4 \cdot 0$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $5$ by $- 3$ .

$- 15 - 4 \cdot 0$

Step 4.1.2

Multiply $- 4$ by $0$ .

$- 15 + 0$

Step 4.2

Add $- 15$ and $0$ .

$- 15$