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Let $T : \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ be the linear transformation that reflects each point through the $x_{1}$ -axis. (See Practice Problem $2 . )$ Make two sketches similar to Figure 6 that illustrate properties $(\mathrm{i})$ and (ii) of a linear transformation.

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 8

Introduction to Linear Transformations

Introduction to Matrices

University of Michigan - Ann Arbor

Idaho State University

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okay. In this question, that given is linear transformation. Yeah, is are Hispanic are to on t reflex each pointed. Be through X to access. Okay. And what we have to do, we have to toe make two sketches similar to figure six that demonstrate properties one and two of the definition off. Linear transformation. So what will be our concept or concept will be, Oh, rotational transformation and properties off linear transformations. Yeah. Okay, so let the X is the simple minus 1001 and x one x two. That is it calls to mind a second extra. Okay, no leg. We can assume I knew the values. So you it wants toe be assumed that 34 and weak was 24 titi. Okay, so from this, you can say u plus v equals to seven and seven. Okay, then BU equals two. My next 1001 t t four. The basic was to minus tree and four. Okay. And TV was too in this 1001 And this will be 43 And this will be minus four today. Okay? And when we okay, try to do be you blustery u plus we. Then it will be minus seven and seven and t zero will be zero. Okay, so what we have to observe in this question that be you? Plus the the equals toe T u plus three. Okay. And what is the observation? Observation is he reflects UV and you plus we about extra access. Okay. What he reflects if labs you the end u plus we about the XTO access. Now we have to make their sketches. And for his sketches, the sketch will be mhm. This is the This is the all these in 00 on. Okay, On the first you will be you will be you will be 34 on we will be. We will be 43 Okay, So you bliss we will be you bliss. We will be 77 Okay, you got that? And similarly, similarly you dash will be minus 34 and V dish will be minus 43 And you bliss U plus V Dash will be minus 77 The result and Victor that will be from here. Okay, so this will be you class. We were Okay, So this are they sketches. And this is our answer. Thank you

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