The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x & 2 &...

Mathematics

JAMB 1998

The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{pmatrix}\) in terms of x is

A. -3x² - 17
B. -3x² + 9x - 1
C. 3x² + 17
D. 3x² - 9x + 5

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Correct Answer: Option B

Explanation

\(\begin{vmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{vmatrix}\) = x\(\begin{vmatrix}2 & 3 \\ 1+x & 4\end{vmatrix}\) - \(\begin{vmatrix}1-x & 3 \\ 1 & 4\end{vmatrix}\) = 0

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

= 5x - 3x² -1 + 4x

= -3x² + 9X - 1

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