22, -T1+T2s/M1SampleA%20(1).pdf6 / 10110%Math 1554, Sample Midterm 1A. Your initials:8. (8 points) Consider the following linear transformation, and answer the questions below. Youdo not need to justify your reasoning.11T(r1, x2) =22(a) What is the domain of T?(b) What is the co-domain of T?(c) What is the standard matrix of T?(d) What are the images of the standard vectors ē and ē2?(e) Is T onto (yes or no)?(f) Is T one-to-one (yes or no)?(g) Draw a sketch of ē1, ë2, T(ēj) and T(e2) on one picture. Clearly label your vectors.MacBook Pro

Answered: Image /qna-images/answer/5858b7cc-c79d-45ca-8956-5bf3c64a31b3.jpg

8. (8 points) Consider the following linear transformation, and answer the questions below. You do not need to justify your reasoning. T(r1, 22) = %3D (a) What is the domain of T? (b) What is the co-domain of T? (c) What is the standard matrix of T? (d) What are the images of the standard vectors e and e2? (e) Is T onto (yes or no)? (f) Is T one-to-one (yes or no)? (g) Draw a sketch of e, e2, T(ëj) and T(e) on one picture. Clearly label your vectors.

8. (8 points) Consider the following linear transformation, and answer the questions below. You do not need to justify your reasoning. T(r1, 22) = %3D (a) What is the domain of T? (b) What is the co-domain of T? (c) What is the standard matrix of T? (d) What are the images of the standard vectors e and e2? (e) Is T onto (yes or no)? (f) Is T one-to-one (yes or no)? (g) Draw a sketch of e, e2, T(ëj) and T(e) on one picture. Clearly label your vectors.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 4EQ

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