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Math 317: Linear Algebra Homework 9 The following problems are for additional practice and are not to be turned in: (All problems come from Linear Algebra: A Geometric Approach, 2nd Edition by ShifrinAdams.) Exercises: Section 4.2: 1–6, 8, 9 Turn in the following problems. 1. Section 4.2, Problem 2d 2. Section 4.2, Problem 6 (Hint: Find a matrix A so that V = R(A). Finding a basis for the orthogonal complement of V should now be straightforward.) 3. Section 4.2, Problem 10 4. Section 4.2, 1 1 5. Let A = 1 0 Problem 11 0 −1 1 2 1 1. and b = 1 1 −3 1 1 1 (a) Determine the QR factorization of A. (b) Use the QR factors from part (a) to determine the least squares solution to Ax = b. 6. (a) Explain what happens when the Gram-Schmidt process is applied to an orthronormal set of vectors. (b) Explain what happens when the Gram-Schmidt process is applied to a linearly dependent set of vectors. 1