Find a matrix $P$ which transforms the following matrices to diagonal form. Hence calculate the power matrix. 1. If $A = \begin{bmatrix} 3 & -1 & 1 \ -1 & 5 & -1 \ 1 & -1 & 3 \end{bmatrix}$, calculate $A^4$.
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The eigenvalues are the solutions to the characteristic equation, which is given by det(A - λI) = 0, where I is the identity matrix and λ are the eigenvalues. For matrix A = [3 -1; -1 3], the characteristic equation is: (3 - λ)^2 - (-1)^2 = 0 λ^2 - 6λ + 8 = Show more…
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