The determinant of matrix begin pmatrix x amp 1... - JAMB Mathematics 1998 Question
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
correct option: b
\(\begin{vmatrix} x & 1 & 0 \ 1-x & 2 & 3 \ 1 & 1+x & 4\end{vmatrix}\) = 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
= 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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