Evaluate (begin{vmatrix} 4 & 2 & -1 \ 2 & 3 & -1 \ -1 & 1 & 3 end{vmatrix})
-
A.
25 -
B.
45 -
C.
15 -
D.
55
Correct Answer: Option A
Explanation
(begin{vmatrix} 4 & 2 & -1 \ 2 & 3 & -1 \ -1 & 1 & 3 end{vmatrix})
4 (begin{vmatrix} 3 & -1 \ 1 & 3 end{vmatrix}) -2 (begin{vmatrix} 2 & -1 \ -1 & 3end{vmatrix}) -1 (begin{vmatrix} 2 & 3 \ -1 & 1 end{vmatrix})
4[(3 x 3) – (-1 x 1)] -2 [(2x 3) – (-1 x -1)] -1 [(2 x 1) – (-1 x 3)]
= 4[9 + 1] -2 [6 – 1] -1 [2 + 3]
= 4(10) – 2(5) – 1(5)
= 40 – 10 – 5
= 25