Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 8. 1 1 -9 1 A = 10 1 -1 -9 a. The orthogonal projection of b onto Col A is 6 = (Simplify your answer.)

The set of polynomials s a basis for IP2. Find the coordinate vector of elative to B. [p(t)]B = B = {3-4t,t−3+t²,− (7+7t+5t²)} p(t) = −3+(-2)t + 3t² in Cocalc). To solve this problem, you will at some point end up solving a system of linear equations; feel free to do that with a computer (e.g.,

Describe all least-squares solutions of the equation Ax = b. 110 1 1 1 0 5 A = #-0 10 1 4 101 8 The least-squares solutions are all vectors of the form x = (Simplify your answers.) +x3, with x3 free.

A QR-decomposition of A is given. Use it to find the least squares solution of Ax = b. A = 1 75 752√5 75 3 0 √5 √5 b = Enter the components of the least squares solution x = [x y] into the answer box below (in order), separated with a comma.

Use the factorization A = QR to find the least-squares solution of Ax = b. 2 3 A = 2 4 2 -8 b = 6 8 Sa N|m 3 3 2 2 3 3 5 01 ANEE (Simplify your answer.)