Explain how to comple by showing steps: Consider the linear transformation from R² to R² known as "rotation by -90 de-grees."The matrix of this transformation isIs this transformation onto ?Is this transformation injective (one-to-one) ?What is the image of01[28]0?If there is an inverse for this transformation, what is the matrix of the inverse?

Answered: Image /qna-images/answer/24982c4b-425c-4bde-9157-9100f6b83e3c.jpg

Answered: Consider the linear transformation from…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 37EQ

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1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .
Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.
Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).
The figure shows three outline versions of the letter F. The second one is obtained from the first by shrinking horizontally by a factor of 0.75, and the third is obtained from the first by shearing horizontally by a factor of 0.25. a Find a data matrix D for the first letter F. b Find a transformation matrix T that transforms the first F into the second. Calculate TD, and verify that this is a data matrix for the second F. c Find the transformation matrix S that transforms the first F into the third. Calculate SD, and verify that this is a data matrix for the third F.
Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 8.
In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 7.
a Let T=[3001]. What effect does T have on the gray square in Table 1? b Let S=[1002]. What effect does S have on the gray square in Table 1? c Apply S to the vertices of the square, and then apply T to the result. What is the effect of the combined transformation? d Find the product matrix W=TS. e Apply the transformation W to the square. Compare to you final result in part c. What do you notice?
Consider the linear transformation from R² to R² known as “"rotation by -90 de- grees." The matrix of this transformation is Is this transformation onto ? Is this transformation injective (one-to-one) ? What is the image of 0 1 [99] -1 0 1 2 ? If there is an inverse for this transformation, what is the matrix of the inverse?
If f and g are linear transformations are represented by the matrices (0 -4/2 1) and (3 3/-5 -4), what is the image of the point (-1,1) under the composite transformation g o f?
Is M1 a linear transformation? Justify your answer
Find the standard matrix of the composition of linear transformations in R? described by: reflection about the y-axis, followed by a clockwise rotation by 30 degrees (about the origin).

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