4. Define the following complex vector space=a€= (²x² = a +d=0}with the usual addition and scalar multiplication.(a) Find an appropriate value of r such that V~ Cr.(b) Give an explicit isomorphism T: V→ Cr. Make sure to prove that T is anisomorphism!

Answered: Image /qna-images/answer/e7b679f7-aefc-48be-9cbe-3e6413d88d1e.jpg

Answered: Define the following complex vector…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 69E: Find a basis for R2 that includes the vector (2,2).

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Define the following complex vector space a *-{[%]₁ = C d=0} € C2x2: a- :a+d= with the usual addition and scalar multiplication. (a) Find an appropriate value of r such that V~ Cr. (b) Give an explicit isomorphism T: V→ Cr. Make sure to prove that T is an isomorphism!