Set B = toeplitz(0 : −1 : −3, 0 : 3) The matrix B is not symmetric and hence it is not guaranteed to be diagonalizable. Use MATLAB to verify that the rank of B equals 2. Explain why 0 must be an eigenvalue of B and the corresponding eigenspace must have dimension 2. Set [X,D] = eig(B). Compute X−1BX and compare the result with D. Compute also XD5X−1 and compare the result with B5.

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