Question: Please explain fully so I can understand Let -2 0 IN A = -1 0 (a) Find the characteristic polynomial of A. (b) Find the

Please explain fully so I can understand

Let -2 0 IN A = -1 0 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find the corresponding eigenvectors to each eigenvalue of A. (d) Find the corresponding eigenspace to each eigenvalue of A. (e) Find a basis for each of the corresponding eigenspace. (f) Find the dimension of the eigenspace of each eigenvector. (g) Determine whether Theorem 7.6 (sufficient condition for Diagonalization) is applicable. (h) Determine whether A is diagonalizable. If it is, find the resulting diagonal matrix. (i) Define the linear transformation T : R3 - R3 as T(v) = Av, where v = (x, y, z). If possible, find a basis B for R3 such that the matrix of T relative to the basis B is diagonal

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