If the adjoint of a 3 × 3 matrix P is \left[\right. 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \left]\right. , then the possible value(s) of the determinant of P is(are)

Engineering

Mathematics

Adjoint of a Matrix

Question

If the adjoint of a 3 × 3 matrix P is $[\begin{matrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{matrix}]$ , then the possible value(s) of the determinant of P is(are)

– 1

– 2

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$adj (P) = [\begin{matrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{matrix}]$

$| adj (P) | = | \begin{matrix} 1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3 \end{matrix} | = | \begin{matrix} 0 & 3 & 1 \\ 0 & - 1 & 1 \\ 1 & 1 & 3 \end{matrix} | = 4$

| adj(P) | = | P |² = 4 $\Rightarrow$ P = ±2.

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