WBJEE · Maths · Matrices
If \(I=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)\) and \(P=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -2\end{array}\right)\) Then, the matrix \(P^{3}+2 P^{2}\) is equal to
- A P
- B I-P
- C \(2I+P\)
- D \(2I-P\)
Answer & Solution
Correct Answer
(C) \(2I+P\)
Step-by-step Solution
Detailed explanation
Given, \(I=\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)\) and \(P=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -2\end{array}\right)\) The characteristic equation of \(P\) is \[ |P-\lambda|=0 \]…
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