Question: 5. (5 points) Let A 6 RM be symmetric. Prove that we can nd a symmetric matrix B 6 RM with A = B2 if

$5. (5 points) Let A 6 RM\" be symmetric. Prove$

5. (5 points) Let A 6 RM\" be symmetric. Prove that we can nd a symmetric matrix B 6 RM\" with A = B2 if and only if all the eigenvalues of A are nonnegative. Hint: use the spectral theorem for this problem1 and the fact that C?) = A?) :3 '0ch = A||v||2

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