find the characteristics equation of the matrixes[1 -2 3 0]
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) Let A be the matrix A = 1 1 1
1 1 0
0 01
a) Find the characteristic equation for A and use it to find the eigenvalues of A. b) Find the eigenvectors corresponding to each of the eigenvalue found in part a) c) Construct the diagonal matrix D with eigenvalues on the diagonal d) Construct the matrix P of eigenvectors. Hint: make sure the eigenvectors are in the same order as the eigenvalues e) Show that P D = AP by multiplying the matrices involved f) Find P −1 and then show that P −1AP is equal to the diagonal matrix of part c)
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