Verify Cayley Hamilton theorem for the given matrix \( B \) and hence find \( B^{-1} \) and \( B^{4} \). \[ B=\left[\begin{array}{ccc} 13 & -3 & 5 \\ 0 & 4 & 0 \\ -15 & 9 & -7 \end{array}\right] \]
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The characteristic polynomial of a matrix is given by the determinant of (B - λI), where I is the identity matrix and λ are the eigenvalues. So, we have: B - λI = \[ \begin{array}{ccc} 13-λ & -3 & 5 \\ 0 & 4-λ & 0 \\ -15 & 9 & -7-λ \end{array} \] Taking the Show more…
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