Consider the following matrix. 4 12 A= -18 2 -14 -2 13 19 11 21 -4 -4 - 12 4 8 8 a. Compute the SVD(singular valued deco

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Consider The Following Matrix 4 12 A 18 2 14 2 13 19 11 21 4 4 12 4 8 8 A Compute The Svd Singular Valued Deco 1 (77.52 KiB) Viewed 26 times

Consider the following matrix. 4 12 A= -18 2 -14 -2 13 19 11 21 -4 -4 - 12 4 8 8 a. Compute the SVD(singular valued decomposition) of A. Compute A1, the best rank-1 approximation of A. b. Show that each row of A1 is the projection of each row of A onto Vì, the first right singular vector A. Similarly, show that each column of A1 is the projection of each column of A onto uị, the first left singular vector of A. a C. Compute A+ and use it to compute a projection matrix that projects onto C(A). Is At a left inverse of A, right inverse of A, or neither? Compute the projection p of the vector b = (40, 20, 10,0) onto C(A). d. Solve two systems of equations using the pseudoinverse A+ (do not call np. linalg. lstsq): Ax = p and Ax = b. Verify that the solution to the former is exact while the solution to the latter is a least-square solution.