Answered: 3x Is T a linear trans- 2x-y formation?…

3x Is T a linear trans- 2x-y formation? Justify your answer. If T is a linear transformation find its matrix relative to the standard basis of R². 7.5. Let T : R2 → R² be defined by T X =

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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Question

I need your assistance in solving this problem using only matrix notation. I'm facing difficulties in finding the solution without employing any other methods. Can you please provide a detailed explanation, step-by-step, using matrix notation exclusively?

this has to be done in the matrix way

Furthermore, I have attached both of the questions and answer. Could you demonstrate the matrix approach leading to the solution?

워
7.6 No. T(e1 + ez) = V2, but T(e1) + T(E2) = 2.
[m=3
7.5 Yes. [T]

X
3x
7.5. Let T: R² → R² be defined by T
Is T a linear trans-
y
2x - y
formation? Justify your answer. If T is a linear transformation find its matrix
relative to the standard basis of R².
=
3
7.6. Let T: R³ → R be given by T(v) = ||v||, where ||v|| is the length the vector
v. Is T a linear transformation?

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Step 2: Check T is linear transformation or not

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