The determinant of matrix (begin{pmatrix} x & 1 & 0 \ 1-x & 2 & 3 \ 1 & 1+x & 4end{pmatrix}) in terms of x is
-
A.
-3x2 – 17 -
B.
-3x2 + 9x – 1 -
C.
3x2 + 17 -
D.
3x2 – 9x + 5
Correct Answer: Option B
Explanation
(begin{vmatrix} x & 1 & 0 \ 1-x & 2 & 3 \ 1 & 1+x & 4end{vmatrix}) = x(begin{vmatrix}2 & 3 \ 1+x & 4end{vmatrix}) – (begin{vmatrix}1-x & 3 \ 1 & 4end{vmatrix}) = 0
= x[8 – 3(1 + x)] – [4(1 – x)-3] – 0 = x[5 – 3x] – [1 – 4x]
= 5x – 3x2 -1 + 4x
= -3x2 + 9X – 1