1. Let V = M22(Q), the vector space of 2 x 2 matrices with rational coefficients. Decide which of the following subsets of V is a vector subspace of V. In each case, either give a proof that it is a subspace or demonstrate an axiom that is not satisfied. : 2a – b = c +d}, -{(.:: :) :asco}. a b с d {(: :) W1 = W2 = : ас %— a b W4 = | : (a – e)(b – d) = 0 } .

1. Let V = M22(Q), the vector space of 2 x 2 matrices with rational coefficients. Decide which of the following subsets of V is a vector subspace of V. In each case, either give a proof that it is a subspace or demonstrate an axiom that is not satisfied. : 2a – b = c +d}, -{(.:: :) :asco}. a b с d {(: :) W1 = W2 = : ас %— a b W4 = | : (a – e)(b – d) = 0 } .

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 4EQ: In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In...

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