Question

If \(\left|\begin{array}{ccc}-1 & 7 & 0 \\ 2 & 1 & -3 \\ 3 & 4 & 1\end{array}\right|=A\), then \(\left|\begin{array}{ccc}13 & -11 & 5 \\ -7 & -1 & 25 \\ -21 & -3 & -15\end{array}\right|\) is
(A) \(A^{2}\)
(B) \(A^{2}-A+I_{3}\)
(C) \(A^{2}-3 A+I_{3}\)
(D) \(3 A^{2}+5 A-4 I_{3}\)

Answer 1

Ans: (A)
Hint : \(P=\left[\begin{array}{ccc}-1 & 7 & 0 \\ 2 & 1 & -3 \\ 3 & 4 & 1\end{array}\right]\)
then adj \(P=\left[\begin{array}{ccc}13 & -11 & 5 \\ -7 & -1 & 25 \\ -21 & -3 & -15\end{array}\right]\)
\(A=|P|\) and \(A^{2}=|\operatorname{Adj}(P)|^{2}\)

Answer 2

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Answer 3

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