9. Suppose we are solving for Arb with A E Rmxn being rank deficient (minimum norm...

Transcribed Image Text:

9. Suppose we are solving for Arb with A E Rmxn being rank deficient (minimum norm solution) (a) For b(A) why wouldn't the solution (ATA)-¹Ab work? (b) Suppose beR(A). Show that the error vector is indeed zero in this case. (c) Say, be R(A). Verify that the minimum norm solution that we obtained in the class is indeed a solution. Also show that the choice of null space basis vectors from M(A) and (AT) doesn't affect the error. (d) Comment on the uniqueness of SVD in light of your answer to the above question. (e) Letr be the rank of A and let r-1 singular values repeat. What can you say about uniqueness of SVD in this case? 9. Suppose we are solving for Arb with A E Rmxn being rank deficient (minimum norm solution) (a) For b(A) why wouldn't the solution (ATA)-¹Ab work? (b) Suppose beR(A). Show that the error vector is indeed zero in this case. (c) Say, be R(A). Verify that the minimum norm solution that we obtained in the class is indeed a solution. Also show that the choice of null space basis vectors from M(A) and (AT) doesn't affect the error. (d) Comment on the uniqueness of SVD in light of your answer to the above question. (e) Letr be the rank of A and let r-1 singular values repeat. What can you say about uniqueness of SVD in this case?

Answer rating: 100% (QA)

question 9 a The solution ATAATb will not work for finding the minimum norm solution of a system of linear equations represented by a matrix A and a righthand side vector b when A is rank deficient Th... View the full answer