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Determine whether such a matrix A exists. If yes, find an example of A, if no, justify your answer. (a) ATA has an eigenvector (2, 1) corresponding to the eigenvalue 6 , and AAT has two eigenvectors (2, −1, 1) and (1, 1, 0) corresponding to eigenvalues 6 and 5 , respectively. (b) ATA has an eigenvector (2, 1) corresponding to the eigenvalue 6 , and AAT has two eigenvectors (2, −1, 1) and (1, 2, 0) corresponding to eigenvalues 6 and 5 , respectively.

Determine whether such a matrix A exists. If yes, find an example of A, if no, justify your answer. (a) ATA has an eigenvector (2, 1) corresponding to the eigenvalue 6 , and AAT has two eigenvectors (2, −1, 1) and (1, 1, 0) corresponding to eigenvalues 6 and 5 , respectively. (b) ATA has an eigenvector (2, 1) corresponding to the eigenvalue 6 , and AAT has two eigenvectors (2, −1, 1) and (1, 2, 0) corresponding to eigenvalues 6 and 5 , respectively.

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Determine whether such a matrix A exists. If yes, find an example of A , if no, justify your answer. (a) A T A has an eigenvector ( 2 , 1 ) corresponding to the eigenvalue 6 , and A A T has two eigenvectors ( 2 , − 1 , 1 ) and ( 1 , 1 , 0 ) corresponding to eigenvalues 6 and 5 , respectively. (b) A T A has an eigenvector ( 2 , 1 ) corresponding to the eigenvalue 6 , and A A T has two eigenvectors ( 2 , − 1 , 1 ) and ( 1 , 2 , 0 ) corresponding to eigenvalues 6 and 5 , respectivelyd

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