Let T: R? » P2(R) and U : R' → M2x2 (R) be lincar transformations. A student claims U must be invertible because dim(Rª) = dim(M2x2 (R)). If the student is correct, prove their claim. If the student is not correct, explain why and give an example to illustrate. Clearly state whether or not the student is correct as part of your solution.

Let T: R? » P2(R) and U : R' → M2x2 (R) be lincar transformations. A student claims U must be invertible because dim(Rª) = dim(M2x2 (R)). If the student is correct, prove their claim. If the student is not correct, explain why and give an example to illustrate. Clearly state whether or not the student is correct as part of your solution.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 29E

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