Finite Math Examples

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

The determinant of $[\begin{array}{c} 2 & 1 & 2 \\ 0 & 3 & 2 \\ 3 & 4 & 2 \end{array}]$ is $- 16$ .

Tap for more steps...

Set up the determinant by breaking it into smaller components.

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

The determinant of $2 | \begin{array}{c} 3 & 2 \\ 4 & 2 \end{array} |$ is $- 4$ .

Tap for more steps...

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

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

Simplify the determinant.

Tap for more steps...

Simplify each term.

Tap for more steps...

Multiply $3$ by $2$ to get $6$ .

$2 (6 - 4 \cdot 2) + 0 | \begin{array}{c} 1 & 2 \\ 4 & 2 \end{array} | + 3 | \begin{array}{c} 1 & 2 \\ 3 & 2 \end{array} |$

Multiply $- 4$ by $2$ to get $- 8$ .

$2 (6 - 8) + 0 | \begin{array}{c} 1 & 2 \\ 4 & 2 \end{array} | + 3 | \begin{array}{c} 1 & 2 \\ 3 & 2 \end{array} |$

Simplify the expression.

Tap for more steps...

Subtract $8$ from $6$ to get $- 2$ .

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

Multiply $2$ by $- 2$ to get $- 4$ .

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

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

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

The determinant of $3 | \begin{array}{c} 1 & 2 \\ 3 & 2 \end{array} |$ is $- 12$ .

Tap for more steps...

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

$- 4 + 0 + 3 ((1) (2) - 3 \cdot 2)$

Simplify the determinant.

Tap for more steps...

Simplify each term.

Tap for more steps...

Multiply $2$ by $1$ to get $2$ .

$- 4 + 0 + 3 (2 - 3 \cdot 2)$

Multiply $- 3$ by $2$ to get $- 6$ .

$- 4 + 0 + 3 (2 - 6)$

Simplify the expression.

Tap for more steps...

Subtract $6$ from $2$ to get $- 4$ .

$- 4 + 0 + 3 \cdot - 4$

Multiply $3$ by $- 4$ to get $- 12$ .

$- 4 + 0 - 12$

Add $- 4$ and $0$ to get $- 4$ .

$- 4 - 12$

Subtract $12$ from $- 4$ to get $- 16$ .

$- 16$

Enter YOUR Problem