Question
Determine the value of x, for which the matrix, P
is singular.
Answer :
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To determine the value of \( x \) for which the matrix \( P \) is singular, we need to find when the determinant of \( P \) is zero. A matrix is singular if and only if its determinant is zero. Given the matrix: \[ P = \begin{bmatrix} 3 - x & 2 & 2 \\ 2 & 4 - x & 1 \\ -2 & -4 & -1 - x \end{bmatrix} \] The determinant of \( P \) is calculated as follows: \[ \det(P) = (3 - x) \left( (4 - x)(-1 - x) - (1)(-4) \right) - 2 \left( 2(-1 - x) - (1)(-2) \right) + 2 \left( 2(-4) - (4 - x)(-2) \right) \] Let's
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