Solved: In Exercises 17 and 18, A is an m × n matrix and b

Chapter 6, Problem 18E

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In Exercises 17 and 18, A is an m × n matrix and b is in Rm. Mark each statement True or False. Justify each answer.a. If b is in the column space of A, then every solution of Ax = b is a least-squares solution.b. The least-squares solution of Ax = b is the point in the column space of A closest to b.c. A least-squares solution of Ax = b is a list of weights that, when applied to the columns of A, produces the orthogonal projection of b onto Col A. e. The normal equations always provide a reliable method for computing least-squares solutions.f. If A has a QR factorization, say A = QR, then the best way to find the least-squares solution of Ax = b is to compute

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