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2 1 8. Let W = span . Use the Gram-Schmidt process to produce an orthogonal 2 ' 2 1 2 basis for W. Then use this reSult to produce an orthonormal basis for W. 9. Use the Gram-Schmidt process to nd an orthogonal basis for the column space of 1 4 3 _ 2 2 O A _ 1 3 2 ' 4 1 3 10. Use the Gram-Schmidt process to nd an orthogonal basis for the column space of 1 4 3 1 _ 2 2 0 1 B _ 1 3 2 1 ' 4 1 3 1 4 11. Let B be the matrix in problem 10. Find the orthogonal projection of v = _32 onto C018. 1 4 12. Use the result of problem 10 to nd the orthogonal projection of v = _32 onto NulB T. 1 13. Use a system of normal equations to nd the least squares solution to Ax = b where A = 1 4 2 2 2 _ 3 1 _3 and b _2 . 4 1 1 14. Is the vector found in problem 13 a solution to Ax = b? 15. Use a system of normal equations to nd the least squares solution to Ax = b where A = 1 4 2 2 2 _ 2 1 _3 andb _1 . 4 1 7 16. Is the vector found in problem 15 a solution to Ax = b? 17. Let A and b be given as in problem 13. Use a system of normal equations to nd projaIAb. 1 _32 . Give the number of least squares 2 18. Let B be given as on problem 10 and let y = solutions to Bx = y