1. True or False a) If A is an mxn matrix, such that Ax=0 for every vector x in R, then A is the mxn zero matrix. b) The row echelon form of an invertible 3x3 matrix is invertible. c) If A is an mxn matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly indépendant. d) If T is the linear transformation whose standard matrix is an mxn matrix A and the columns of A are linearly independent, then T is 1-to-1 e) If T is the linear transformation whose standard matrix is an mxn matrix A and the columns of A are linearly independent, then T is onto f) If T is the linear transformation whose standard matrix is an mxn matrix A, where m

1. True or False a) If A is an mxn matrix, such that Ax=0 for every vector x in R, then A is the mxn zero matrix. b) The row echelon form of an invertible 3x3 matrix is invertible. c) If A is an mxn matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly indépendant. d) If T is the linear transformation whose standard matrix is an mxn matrix A and the columns of A are linearly independent, then T is 1-to-1 e) If T is the linear transformation whose standard matrix is an mxn matrix A and the columns of A are linearly independent, then T is onto f) If T is the linear transformation whose standard matrix is an mxn matrix A, where m

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 28EQ: Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises...

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