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Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax=b have at least one solution for every possible b? Explain. Yes. A has a free variable. So the free variable can equal any value such that there is at least one solution for every possible b. O Yes. Since A has three rows and two pivots, there is a row without a pivot. So there is at least one solution for every possible b. O No. A has one free variable, so there will be no solution to the system for any possible b No. Since A has three rows and two pivots, there is a row without a pivot. To have at least one solution for every possible b, all rows of A must have a pivot.

Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax=b have at least one solution for every possible b? Explain. Yes. A has a free variable. So the free variable can equal any value such that there is at least one solution for every possible b. O Yes. Since A has three rows and two pivots, there is a row without a pivot. So there is at least one solution for every possible b. O No. A has one free variable, so there will be no solution to the system for any possible b No. Since A has three rows and two pivots, there is a row without a pivot. To have at least one solution for every possible b, all rows of A must have a pivot.

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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Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax=b have at least one solution for every possible b? Explain. O Yes. A has a free variable. So the free variable can equal any value such that there is at least one solution for every possible b. Yes. Since A has three rows and two pivots, there is a row without a pivot. So there is at least one solution for every possible b. No. A has one free variable, so there will be no solution to the system for any possible b No. Since A has three rows and two pivots, there is a row without a pivot. To have at least one solution for every possible b, all rows of A must have a pivot.
Transcribed Image Text:Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax=b have at least one solution for every possible b? Explain. O Yes. A has a free variable. So the free variable can equal any value such that there is at least one solution for every possible b. Yes. Since A has three rows and two pivots, there is a row without a pivot. So there is at least one solution for every possible b. No. A has one free variable, so there will be no solution to the system for any possible b No. Since A has three rows and two pivots, there is a row without a pivot. To have at least one solution for every possible b, all rows of A must have a pivot.
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