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1. Which of the following vectors is not a linear combination of and 3 1) |3)| [:] [:] 2) '4) 5) all of them

1. Which of the following vectors is not a linear combination of and 3 1) |3)| [:] [:] 2) '4) 5) all of them

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 24EQ
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1. Which of the following vectors is not a linear combination of and 1» [ ] 3 2): 3) [2] '4) 5) all of them 2. Suppose A is an m x n matrix, x ɛ R" and Ax = b. Then b is in 1) R" | 2) R*T 3) R™†ªT4) R*n 3. Consider the statements below. (I) For each b in R" the equation Ax = b has a solution. (II) Each b in R" is a linear combination of the columns of A. (III) The columns of A span Rm. (IV) A has a pivot in each row. Which one of the four statements is not equivalent to the others? ( 1) I] 2) II| 3) I | 4) IV
Transcribed Image Text:1. Which of the following vectors is not a linear combination of and 1» [ ] 3 2): 3) [2] '4) 5) all of them 2. Suppose A is an m x n matrix, x ɛ R" and Ax = b. Then b is in 1) R" | 2) R*T 3) R™†ªT4) R*n 3. Consider the statements below. (I) For each b in R" the equation Ax = b has a solution. (II) Each b in R" is a linear combination of the columns of A. (III) The columns of A span Rm. (IV) A has a pivot in each row. Which one of the four statements is not equivalent to the others? ( 1) I] 2) II| 3) I | 4) IV
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