Question

(a)Find the matrices M and N that satisfy the pair of equations M-D N=\left[\begin{array}{rr} A & -5 \\ -8 & 0 \\ 2 & 5 \end{array}\right] \text { and }

M+D N=\left[\begin{array}{rr} 1 & 12 \\ 1 & B \\ 3 & 14 \end{array}\right] \text { (i) Evaluate the inverse of the matrix } P=\left[\begin{array}{ll} A & 1 \\ 1 & A \end{array}\right] \text {. } (ii)Find the eigenvalues of the matrix P. (iii) For each eigenvalue find the associated eigenvector.

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