Please do not use computational methodssoftware 4

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Unformatted text preview: ase do not use computational methods/software) 4. Determine whether or not the following matrix it. Otherwise, explain why. -1 1 12 1 B= 6 5 3 -4 is diagonalizable. If it is, then diagonalize -2 -4 4 9 -2 -4 5 10 (Hint: it is known that 2 is an eigenvalue of B.) 5. Suppose that A and B are similar matrices. (a) Prove that A3 and B 3 are similar matrices. (b) Suppose also that A is non-singular. Prove that A-1 and B -1 are similar. 6. Prove that if is an eigenvalue of non-singular matrix A, then 1 is an eigenvalue of A-1 . 1...
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