Let a = [4 - 5 - 32]. Calculate a ^ 3 by using eigenvalues and eigenvectors of matrix The values of matrix A are from left to right and from top to bottom | Math enthusiast | Mathematical art

Let a = [4 - 5 - 32]. Calculate a ^ 3 by using eigenvalues and eigenvectors of matrix The values of matrix A are from left to right and from top to bottom

|A - λ e | = (7 - λ) (1 + λ) so the eigenvalue of a is 7, the basic solution system of - 1 (a-7e) x = 0 is A1 = (5, - 3) ^ t (a + e) x = 0, and the basic solution system is A2 = (1,1) ^ t, let P = (A1, A2) = 51-31, then p ^ - 1AP = diag (7, - 1) so a = pdiag (7, - 1) P ^ - 1, so a ^ 3 = pdiag (7 ^ 3, - 1) P ^ - 1 = (5 * 7 ^

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