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2. Let Ax = b be a system of linear equations in variables. Designate the columns of A as a, a, a, a, If b is a linear combination of these n column vectors, explain why this implies that the linear system is consistent. Illustrate your answer with an appropriate example. What can you conclude about the linear system if b is not a linear combination of the columns of A?

2. Let Ax = b be a system of linear equations in variables. Designate the columns of A as a, a, a, a, If b is a linear combination of these n column vectors, explain why this implies that the linear system is consistent. Illustrate your answer with an appropriate example. What can you conclude about the linear system if b is not a linear combination of the columns of A?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 4CC
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2. Let Ax = b be a system of linear equations in variables. Designate the columns of A as a, a, a, a, If b is a linear combination of these n column vectors, explain why this implies that the linear system is consistent. Illustrate your answer with an appropriate example. What can you conclude about the linear system if b is not a linear combination of the columns of A?
Transcribed Image Text:2. Let Ax = b be a system of linear equations in variables. Designate the columns of A as a, a, a, a, If b is a linear combination of these n column vectors, explain why this implies that the linear system is consistent. Illustrate your answer with an appropriate example. What can you conclude about the linear system if b is not a linear combination of the columns of A?
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