Let A = PDP-1, where P is orthogonal and D is diagonal, and let a be an eigenvalue of A of multiplicity k. Then 2 appears k times on the diagonal of D. Explain why the dimension of the eigenspace for 2 is k.

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A: Please refer the attached image for complete solution. THANK YOU.

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Q: Suppose that A = a= b [0 a has eigenvalues -3 and 3. What are the values of a and b?

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A: We will solve this by Counter example

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Q: Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. -[: 와 21 = 4, x1 =…

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Q: Confirm by multiplication that x is an eigenvector of A, and find the corresponding eigenvalue. 301…

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Q: Find a basis for the eigenspace corresponding to the eigenvalue. -6 A = =D9 - 4

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Q: Prove that if B is symmetric, then ||B||is the largest eigenvalue of B.

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Q: Show that A is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue.

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Q: Show that A is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue.

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