Home » » If $$\left|\begin{array}{lll} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{array}\right| = 132$$, find the value of x....

# If $$\left|\begin{array}{lll} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{array}\right| = 132$$, find the value of x....

### Question

If $$\left|\begin{array}{lll} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{array}\right| = 132$$, find the value of x.

A) 5

B) 8

C) 6

D) 3

### Explanation:

$$\left|\begin{array}{lll} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{array}\right| = 132$$
$$\implies 2 \begin{vmatrix} 1 & 4 \\ 3 & 2 \end{vmatrix} - (-5) \begin{vmatrix} x & 4 \\ 0 & 2 \end{vmatrix} + 3 \begin{vmatrix} x & 1 \\ 0 & 3 \end{vmatrix} = 132$$
$$2(2 - 12) + 5(2x) + 3(3x) = 132$$
$$-20 + 10x + 9x = 132$$
$$19x = 152$$
$$x = 8$$

## Dicussion (1)

• $$\left|\begin{array}{lll} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{array}\right| = 132$$
$$\implies 2 \begin{vmatrix} 1 & 4 \\ 3 & 2 \end{vmatrix} - (-5) \begin{vmatrix} x & 4 \\ 0 & 2 \end{vmatrix} + 3 \begin{vmatrix} x & 1 \\ 0 & 3 \end{vmatrix} = 132$$
$$2(2 - 12) + 5(2x) + 3(3x) = 132$$
$$-20 + 10x + 9x = 132$$
$$19x = 152$$
$$x = 8$$