The determinant of matrix ⎛⎜⎝x101−x2311+x4⎞⎟⎠ ( x 1 0 1 − x 2 3 1 1 + x 4 ) in terms of x is

Question 1 Report

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

-3x2 - 17

-3x2 + 9x - 1

3x2 + 17

3x2 - 9x + 5

Answer Details

$| \begin{matrix} x & 1 & 0 \\ 1 - x & 2 & 3 \\ 1 & 1 + x & 4 \end{matrix} |$ = x $| \begin{matrix} 2 & 3 \\ 1 + x & 4 \end{matrix} |$ - $| \begin{matrix} 1 - x & 3 \\ 1 & 4 \end{matrix} |$ = 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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