4. Problem 4: For positive integers m and n, let Mn denote the set of all mxn matrices. We define uev as matrix addition defined in chapter 2 and cou as scalar matrix multiplication defined in chapter 2. Is M a vector space? For two arbitrary vectors in M : 2x2 b a u = and V = y c d (a) Show there is a zero vector, 0, in M such that v 0 =v. 2x2 (b) Carefully show that (s+r)Ou=sou®tOu for scalars s and t. (c) Carefully show that so(tOu)= (st)Ou for scalars s and t.

4. Problem 4: For positive integers m and n, let Mn denote the set of all mxn matrices. We define uev as matrix addition defined in chapter 2 and cou as scalar matrix multiplication defined in chapter 2. Is M a vector space? For two arbitrary vectors in M : 2x2 b a u = and V = y c d (a) Show there is a zero vector, 0, in M such that v 0 =v. 2x2 (b) Carefully show that (s+r)Ou=sou®tOu for scalars s and t. (c) Carefully show that so(tOu)= (st)Ou for scalars s and t.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 63EQ

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