Let A be an m x n matrix, and let b1,..., bk be vectors in R" such that the system b; has a solution x; E R" for each i. Prove that if {b1,..., bk} is linearly independent, then {x1,..., Xx} is linearly independent as well. Ах

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
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Let A be an m × n matrix, and let b1,..., bk be vectors in R" such that the system
b; has a solution x; E R" for each i. Prove that if {b1,...,bx} is linearly
independent, then {x1,..., Xg} is linearly independent as well.
Ах
Ax =
Transcribed Image Text:Let A be an m × n matrix, and let b1,..., bk be vectors in R" such that the system b; has a solution x; E R" for each i. Prove that if {b1,...,bx} is linearly independent, then {x1,..., Xg} is linearly independent as well. Ах Ax =
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