If (begin{vmatrix} 2 & -5 & 3 \ x & 1 & 4 \ 0 & 3 & 2 end{vmatrix} = 132), find the value of x.
-
A.
5 -
B.
8 -
C.
6 -
D.
3
Correct Answer: Option B
Explanation
(begin{vmatrix} 2 & -5 & 3 \ x & 1 & 4 \ 0 & 3 & 2 end{vmatrix} = 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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