Problem 3. Using the randn command in Matlab, form a random 4 2 matrix A. Then...

 

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Problem 3. Using the "randn" command in Matlab, form a random 4 2 matrix A. Then compute the 44 matrix AAT. Using Matlab to compute the eigenvalues of the symmetric matrix AAT, check whether this matrix is positive semidefinite. Then, show mathematically (by hand, not using Matlab) that xTAATx 0 for all vectors x. (Hint: Define z = = AT x.) Problem 3. Using the "randn" command in Matlab, form a random 4 2 matrix A. Then compute the 44 matrix AAT. Using Matlab to compute the eigenvalues of the symmetric matrix AAT, check whether this matrix is positive semidefinite. Then, show mathematically (by hand, not using Matlab) that xTAATx 0 for all vectors x. (Hint: Define z = = AT x.)