c Now let y 1 1 1 T and solve Ax y Comment on how the solution changed d

# C now let y 1 1 1 t and solve ax y comment on how the

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(c) Now let y = 1 . 1 1 T and solve Ax = y . Comment on how the solution changed. (d) Suppose we observe y = Ax + e with k e k 2 = 1. We form an estimate ˜ x = A - 1 y . Which vector e (over all error vectors with k e k 2 = 1) yields the maximum error k ˜ x - x k 2 2 ? (e) Which (unit) vector e yields the minimum error? (f) (Optional) Suppose the components of e are iid Gaussian: e [ i ] Normal(0 , 1) . What is the mean-square error E[ k ˜ x - x k 2 2 ]? (g) (Optional) Verify your answer to the previous part in MATLAB by taking Ax = 1 1 T , and then generating 10 , 000 different realizations of e using the randn command, and then averaging the results. Turn in your code and the results of your computation. 5. Suppose we make a noisy observation of y = Ax , with A = 2 4 - 1 1 - 2 1 4 0 1 5 6 - 1 8 - 4 2 y = 1 2 - 1 - 2 5 (a) Find the total-least squares solution to the above linear inverse problem. (Use MAT- LAB.) (b) What is the residual error k Δ k 2 F ? What are the Δ A and Δ y corresponding to your solution? 3 Last updated 14:22, November 7, 2019
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