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Let A be a 3×3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are not parallel. If a linear system Av = b has infinitely many solutions, what can we say about the third column u3 of A, in terms of u₁ and u₂? In other words, how does u3 relate to u₁ and u₂?

Let A be a 3×3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are not parallel. If a linear system Av = b has infinitely many solutions, what can we say about the third column u3 of A, in terms of u₁ and u₂? In other words, how does u3 relate to u₁ and u₂?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve and show all work, step by step handwritten out. Differential equations and basic linear alegbra should be used for this problem. 

14. Let A be a 3×3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are not parallel. If a linear system Av = b has infinitely many solutions, what can we say about the third column u3 of A, in terms of u₁ and u₂? In other words, how does u3 relate to u₁ and u₂?
Transcribed Image Text:14. Let A be a 3×3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are not parallel. If a linear system Av = b has infinitely many solutions, what can we say about the third column u3 of A, in terms of u₁ and u₂? In other words, how does u3 relate to u₁ and u₂?
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