Part d please (Vector spaces) Let M be the vector space of 2 x 2 matrices with real entries, under the usualaddition and scalar multiplication.F(a) Let N C M be the set of all invertible 2 x 2 matrices. Is N a vector subspace of M ornot? Justify.HABERTAJ(b) Let J: MM be the function given by J(A) = A - AT. Check that J is a lincartransformation. Find a basis for the subspace S = ker(J).(c) Extend your basis from (b) to a basis of M. In other words, find a basis of M that containsyour basis of ker(J) as a subset.(d) Define a function Tr: MR (the trace) by the sum of the diagonal entrics. Check thatTr is a linear transformation. What is the dimension of ker(Tr)?

Answered: Vector space of 2 x 2 matrices with…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...

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