Let A be an invertible matrix of size 3 x 3. Let {x₁, x2. X be a set of three linearly independent vectors in R³. Show that the vectors (Axı, Ax2, Ax3} are linearly independent in R³.

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 invertible matrix of size 3 x 3. Let (X₁, X2, X3) be a set of three
linearly independent vectors in R3. Show that the vectors (Ax₁, Ax2, Ax3} are linearly
independent in R³.
Transcribed Image Text:Let A be an invertible matrix of size 3 x 3. Let (X₁, X2, X3) be a set of three linearly independent vectors in R3. Show that the vectors (Ax₁, Ax2, Ax3} are linearly independent in R³.
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