JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(I\) be an identity matrix of order \(2 \times 2\) and \(P=\left[\begin{array}{cc}2 & -1 \\ 5 & -3\end{array}\right] .\) Then the value of \(n \in N\) for which \(P^n =5 I -8 P\) is equal to ..... .
- A \(8\)
- B \(10\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(P=\left[\begin{array}{cc}2 & -1 \\ 5 & -3\end{array}\right]\) \(5 I-8 P=\left[\begin{array}{ll}5 & 0 \\ 0 & 5\end{array}\right]-\left[\begin{array}{cc}16 & -8 \\ 40 & -24\end{array}\right]=\left[\begin{array}{ll}-11 & 8 \\ -40 & 29\end{array}\right]\)…
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