Question: Linear system 3. Let AER , BER. Show that the nonzero eigenvalues of AB are the same as those of BA. 4. Find the ranks

Linear system

3. Let AER , BER. Show that the nonzero eigenvalues of AB are the same as those of BA. 4. Find the ranks and nullities and provide basis for the range and null spaces of the following matrices: 2 0 0 4 0 0 01 (c) 0 10 0 (a) (b) 0 2 4 0 11 0 0 0 5. Find the diagonal or Jordan canonical forms for the following matrices: 2 0 2 2 240 0 2 11 (a) (b) (9) (d) 2 0 03 -1 0 2 0 0 2 0

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