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Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = 0 have nontrivial solutions? Explain. Yes. Since A has two pivots, there is one free variable. So Ax = 0 has nontrivial solutions. O No. Since A has two pivots, there is one free variable. Since there is at least one free variable, Ax: O has only the trivial solution. Yes. Since A has two pivots, there is one free variable. The solution set of Ax O does not contain the trivial solution if there is at least one free variable. O No. Since A has two pivots, there are no free variables. With no free variables, Ax O has only the trivial solution.

Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = 0 have nontrivial solutions? Explain. Yes. Since A has two pivots, there is one free variable. So Ax = 0 has nontrivial solutions. O No. Since A has two pivots, there is one free variable. Since there is at least one free variable, Ax: O has only the trivial solution. Yes. Since A has two pivots, there is one free variable. The solution set of Ax O does not contain the trivial solution if there is at least one free variable. O No. Since A has two pivots, there are no free variables. With no free variables, Ax O has only the trivial solution.

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 = 0 have nontrivial solutions? Explain. Yes. Since A has two pivots, there is one free variable. So Ax = 0 has nontrivial solutions. O No. Since A has two pivots, there is one free variable. Since there is at least one free variable, Ax: O has only the trivial solution. Yes. Since A has two pivots, there is one free variable. The solution set of Ax O does not contain the trivial solution if there is at least one free variable. AR O No. Since A has two pivots, there are no free variables. With no free variables, O has only the trivial solution. Ax
Transcribed Image Text:Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = 0 have nontrivial solutions? Explain. Yes. Since A has two pivots, there is one free variable. So Ax = 0 has nontrivial solutions. O No. Since A has two pivots, there is one free variable. Since there is at least one free variable, Ax: O has only the trivial solution. Yes. Since A has two pivots, there is one free variable. The solution set of Ax O does not contain the trivial solution if there is at least one free variable. AR O No. Since A has two pivots, there are no free variables. With no free variables, O has only the trivial solution. Ax
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