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Let A be an m x n matrix and b be a vector in Rm. Which of the following is/are true? (Select all that apply) A least-squares solution of Ax = b is a vector & such that |b - Ax|| ≤ b - Ax|| for all x in Rº. The general least-squares problem is to find an x that makes Ax as close as possible to b. If b is in the column space of A, then every solution of Ax = b is a least-squares solution. Any solution of ATAX = ATb is a least-squares solution of Ax = b. A least-squares solution of Ax = b is a vector x that satisfies Ax = b, where b is the orthogonal projection of b onto Col A.

Let A be an m x n matrix and b be a vector in Rm. Which of the following is/are true? (Select all that apply) A least-squares solution of Ax = b is a vector & such that |b - Ax|| ≤ b - Ax|| for all x in Rº. The general least-squares problem is to find an x that makes Ax as close as possible to b. If b is in the column space of A, then every solution of Ax = b is a least-squares solution. Any solution of ATAX = ATb is a least-squares solution of Ax = b. A least-squares solution of Ax = b is a vector x that satisfies Ax = b, where b is the orthogonal projection of b onto Col A.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 36EQ
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Let A be an m x n matrix and b be a vector in Rm. Which of the following is/are true? (Select all that apply) A least-squares solution of Ax = b is a vector such that ||b - Ax|| ≤ b - Ax|| for all x in Rº. The general least-squares problem is to find an x that makes Ax as close as possible to b. If b is in the column space of A, then every solution of Ax = b is a least-squares solution. Any solution of ATAX = ATb is a least-squares solution of Ax = b. A least-squares solution of Ax = b is a vector x that satisfies Ax = b, where is the orthogonal projection of b onto Col A.
Transcribed Image Text:Let A be an m x n matrix and b be a vector in Rm. Which of the following is/are true? (Select all that apply) A least-squares solution of Ax = b is a vector such that ||b - Ax|| ≤ b - Ax|| for all x in Rº. The general least-squares problem is to find an x that makes Ax as close as possible to b. If b is in the column space of A, then every solution of Ax = b is a least-squares solution. Any solution of ATAX = ATb is a least-squares solution of Ax = b. A least-squares solution of Ax = b is a vector x that satisfies Ax = b, where is the orthogonal projection of b onto Col A.
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