4. Suppose A is the same matrix as the previous problem. (1) Compute ATA, and all eigenvalues and eigenvectors of AT A. Is AT A positive definite? (2) Compute AAT, and all eigenvalues and eigenvectors of AAT. Is AAT positive definite? (3) Use (1) and (2) to write down the SVD (Singular Value De- composition) for A. Verify that these eigenvectors exhibit the linear transformations A R4 R³ and AT R³ R4 both as simple stretching.

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