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The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x...

The determinant of matrix (x101x2311+x4) in terms of x is

A.

-3x2 - 17

B.

-3x2 + 9x - 1

C.

3x2 + 17

D.

3x2 - 9x + 5

Correct answer is B

|x101x2311+x4| = x|231+x4| - |1x314| = 0

= x[8 - 3(1 + x)] - [4(1 - x)-3] - 0 = x[5 - 3x] - [1 - 4x]

= 5x - 3x2 -1 + 4x

= -3x2 + 9X - 1