Assume T: R^m to R^n is a matrix transformation with matrix A. Prove that if columns of A are linearly independent, then T is one-to-one. Hint: Remember that matrix transformations satisfy the linearity properties.

Assume T: R^m to R^n is a matrix transformation with matrix A. Prove that if columns of A are linearly independent, then T is one-to-one. Hint: Remember that matrix transformations satisfy the linearity properties.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 55EQ

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Assume T: R^m to R^n is a matrix transformation with matrix A.

Prove that if columns of A are linearly independent, then T is one-to-one.

Hint: Remember that matrix transformations satisfy the linearity properties.

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