Describe the possible echelon forms of the matrix. (a) A is a 3 x 3 matrix with linearly independent columns. (b) A is a 2 x 2 matrix with linearly dependent columns. (c) A is a 4 x 2 matrix, A = [a1 a2], and a2 is not a scalar multiple of a₁. (d) A is a 4 x 3 matrix, A = [a1 a2 a3], the set {a1,2} is linearly independent and as Span{₁, 2}.

Describe the possible echelon forms of the matrix. (a) A is a 3 x 3 matrix with linearly independent columns. (b) A is a 2 x 2 matrix with linearly dependent columns. (c) A is a 4 x 2 matrix, A = [a1 a2], and a2 is not a scalar multiple of a₁. (d) A is a 4 x 3 matrix, A = [a1 a2 a3], the set {a1,2} is linearly independent and as Span{₁, 2}.

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 42EQ

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