Question: Use MATLAB to determine the eigenvalues and eigenvectors for the matrix A = [.5 0 5 .5 0 .8 .8 1 0 0 -1 .9

Use MATLAB to determine the eigenvalues and eigenvectors for the matrix A = [.5 0 5 .5 0 .8 .8 1 0 0 -1 .9 0 1 1 0] If b = (3 0 0 0)^T, will we have lim_k rightarrow infinity A^k b = 0? Why or why not? Find A^10 b and A^20 b. Determine another vector c notequalto 0 that is not a multiple of 6, such that lim_k rightarrow A^k c = 0. Note that choice for c is not unique. Explain your choice for c and calculate A^10 c and A^20 c

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