Find the Determinant [[3,0,0],[5,-9,0],[-9,4,4]]

$[\begin{array}{c} 3 & 0 & 0 \\ 5 & - 9 & 0 \\ - 9 & 4 & 4 \end{array}]$

Set up the determinant by breaking it into smaller components.

$0 | \begin{array}{c} 5 & - 9 \\ - 9 & 4 \end{array} | + 0 | \begin{array}{c} 3 & 0 \\ - 9 & 4 \end{array} | + 4 | \begin{array}{c} 3 & 0 \\ 5 & - 9 \end{array} |$

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

$0 + 0 | \begin{array}{c} 3 & 0 \\ - 9 & 4 \end{array} | + 4 | \begin{array}{c} 3 & 0 \\ 5 & - 9 \end{array} |$

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

$0 + 0 + 4 | \begin{array}{c} 3 & 0 \\ 5 & - 9 \end{array} |$

Find the determinant of $4 | \begin{array}{c} 3 & 0 \\ 5 & - 9 \end{array} |$ .

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

$0 + 0 + 4 ((3) (- 9) - 5 \cdot 0)$

Simplify the determinant.

Simplify each term.

Multiply $3$ by $- 9$ .

$0 + 0 + 4 (- 27 - 5 \cdot 0)$

Multiply $- 5$ by $0$ .

$0 + 0 + 4 (- 27 + 0)$

Simplify the expression.

Add $- 27$ and $0$ .

$0 + 0 + 4 \cdot - 27$

Multiply $4$ by $- 27$ .

$0 + 0 - 108$

Add $0$ and $0$ .

$0 - 108$

Subtract $108$ from $0$ .

$- 108$

Find the Determinant [[3,0,0],[5,-9,0],[-9,4,4]]

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