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Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If an m x n matrix A has a pivot element or a leading 1 on each row then the linear system Ax=b has a unique solution. (b) If an m x n linear system has two solutions x₁, x₂€ R¹, then these are its only solutions. (c) If A and B are nonsingular matrices of order n then AB is nonsingular of order n.

Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If an m x n matrix A has a pivot element or a leading 1 on each row then the linear system Ax=b has a unique solution. (b) If an m x n linear system has two solutions x₁, x₂€ R¹, then these are its only solutions. (c) If A and B are nonsingular matrices of order n then AB is nonsingular of order n.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
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Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If an m x n matrix A has a pivot element or a leading 1 on each row then the linear system Ax=b has a unique solution. (b) If an m x n linear system has two solutions x₁, x₂€ R", then these are its only solutions. (c) If A and B are nonsingular matrices of order n then AB is nonsingular of order n.
Transcribed Image Text:Answer the folowing if it is: ALWAYS TRUE, SOMETIMES TRUE or NEVER TRUE. (a) If an m x n matrix A has a pivot element or a leading 1 on each row then the linear system Ax=b has a unique solution. (b) If an m x n linear system has two solutions x₁, x₂€ R", then these are its only solutions. (c) If A and B are nonsingular matrices of order n then AB is nonsingular of order n.
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