Problem E.1. Consider the following matrix: A = (²₁³) Problem E.1.a. Find the eigenvalue(s) and the eigenvector(s). Problem E.1.b. Is the matrix A diagonalizable? If so, what is the matrix P that diagonalizes A? Problem E.1.c. If the matrix A is diagonalizable, find the diagonal matrix D that is associated to A by calculating D = P.¹AP. Show the work for finding P¹ and for finding the matrix product P-¹AP.

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