Finite Math Examples

$[\begin{array}{c} 0 & 3 & 2 \\ 4 & 3 & 3 \\ 1 & 2 & 0 \end{array}]$

Step 1

Set up the determinant by breaking it into smaller components.

$0 | \begin{array}{c} 3 & 3 \\ 2 & 0 \end{array} | - 4 | \begin{array}{c} 3 & 2 \\ 2 & 0 \end{array} | + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Step 2

Since the matrix is multiplied by $0$ , the determinant is $0$ .

$0 - 4 | \begin{array}{c} 3 & 2 \\ 2 & 0 \end{array} | + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Step 3

Find the determinant of $- 4 | \begin{array}{c} 3 & 2 \\ 2 & 0 \end{array} |$ .

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

$0 - 4 ((3) (0) - 2 \cdot 2) + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Simplify the determinant.

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Simplify each term.

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Multiply $3$ by $0$ .

$0 - 4 (0 - 2 \cdot 2) + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Multiply $- 2$ by $2$ .

$0 - 4 (0 - 4) + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Simplify the expression.

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Subtract $4$ from $0$ .

$0 - 4 \cdot - 4 + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Multiply $- 4$ by $- 4$ .

$0 + 16 + 1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$

Step 4

Find the determinant of $1 | \begin{array}{c} 3 & 2 \\ 3 & 3 \end{array} |$ .

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

$0 + 16 + (3) (3) - 3 \cdot 2$

Simplify the determinant.

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Simplify each term.

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Multiply $3$ by $3$ .

$0 + 16 + 9 - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$0 + 16 + 9 - 6$

Subtract $6$ from $9$ .

$0 + 16 + 3$

Step 5

Add $0$ and $16$ .

$16 + 3$

Step 6

Add $16$ and $3$ .

$19$

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