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9.
Assuming that , find a matrix that orthogonally diagonalizes
10.
Prove that if A is any matrix, then has an orthonormal set of n eigenvectors.
11.
12. matrix and I is the identity matrix, then is orthogonally diagonalizable.
(a) Show that if v is any
(b) Find a matrix P that orthogonally diagonalizes if
Use the result in Exercise 17 of Section 7.1 to prove Theorem 7.3.2a for symmetric matrices.
13.
Indicate whether each statement is always true or sometimes false. Justify your answer by
14. giving a logical argument or a counterexample.
