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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.

Options

A) 5

B) 8

C) 6

D) 3

The correct answer is B.

Explanation:

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

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Dicussion (1)

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

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