Find the Determinant [[2,8,0],[0,1,x],[2,0,0]]

$[\begin{array}{c} 2 & 8 & 0 \\ 0 & 1 & x \\ 2 & 0 & 0 \end{array}]$

Set up the determinant by breaking it into smaller components.

$0 | \begin{array}{c} 0 & 1 \\ 2 & 0 \end{array} | - x | \begin{array}{c} 2 & 8 \\ 2 & 0 \end{array} | + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

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

$0 - x | \begin{array}{c} 2 & 8 \\ 2 & 0 \end{array} | + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

Find the determinant of $- x | \begin{array}{c} 2 & 8 \\ 2 & 0 \end{array} |$ .

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

$0 - x ((2) (0) - 2 \cdot 8) + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $0$ .

$0 - x (0 - 2 \cdot 8) + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

Multiply $- 2$ by $8$ .

$0 - x (0 - 16) + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

Simplify the expression.

Subtract $16$ from $0$ .

$0 - x \cdot - 16 + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

Multiply $- 16$ by $- 1$ .

$0 + 16 x + 0 | \begin{array}{c} 2 & 8 \\ 0 & 1 \end{array} |$

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

$0 + 16 x + 0$

Combine the opposite terms in $0 + 16 x + 0$ .

Add $0$ and $16 x$ .

$16 x + 0$

Add $16 x$ and $0$ .

$16 x$

Find the Determinant [[2,8,0],[0,1,x],[2,0,0]]

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