2. Consider the following matrices and their SVDs 20 B 1. [110] 0 1 = [/8]....

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2. Consider the following matrices and their SVDs √20 B 1.₁ [110] 0 1 = [✓/²8]. A = A = =[], A = U = I, Σ = [2/√6 0 -1/√3] U=1/√6 -1/√2 1/√3 1/√6 1/√2 1/√3] U = 2 2 = -26-8- 2 -1 2 2 3 V: For each of the matrices above: (a) Determine the rank of each matrix (b) Find bases for the four fundamental subspaces (c) Find the pseudoinverse of each matrix Σ = √2 √√3 0 0 Σ = V= - B. 0 " 1 0 V: = 部门 V = 1 司 (d) Form an appropriately sized vector and find the least squares solution to Ax = b. (e) Compute || Ax-b||2/2. (f) Was b € colA? Explain (specifically w.r.t. your answer to the part (e). 2. Consider the following matrices and their SVDs √20 B 1.₁ [110] 0 1 = [✓/²8]. A = A = =[], A = U = I, Σ = [2/√6 0 -1/√3] U=1/√6 -1/√2 1/√3 1/√6 1/√2 1/√3] U = 2 2 = -26-8- 2 -1 2 2 3 V: For each of the matrices above: (a) Determine the rank of each matrix (b) Find bases for the four fundamental subspaces (c) Find the pseudoinverse of each matrix Σ = √2 √√3 0 0 Σ = V= - B. 0 " 1 0 V: = 部门 V = 1 司 (d) Form an appropriately sized vector and find the least squares solution to Ax = b. (e) Compute || Ax-b||2/2. (f) Was b € colA? Explain (specifically w.r.t. your answer to the part (e).