Given that the set S, consisting of all 3x2 matrices with entries in R, forms a vector space under matrix addition and scalar multiplication The subset B of S consists of all matrices of the form: a b+c b C a+b a+c) where a, b, c ER (i) Show that B is a subspace of S. (!!!) (!!) Write down a basis for the vector space B, providing reasons to your answer. State the dimension of the vector space B.

Given that the set S, consisting of all 3x2 matrices with entries in R, forms a vector space under matrix addition and scalar multiplication The subset B of S consists of all matrices of the form: a b+c b C a+b a+c) where a, b, c ER (i) Show that B is a subspace of S. (!!!) (!!) Write down a basis for the vector space B, providing reasons to your answer. State the dimension of the vector space B.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...

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