5. Determine the matrix of the transformation that first reflects points through the horizontal x-axisand then reflects points through the line y = x.

Answered: 5. Determine the matrix of the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...

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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).
Find the matrix of a linear transformation that would take the line 2x -5y = 0 to 7x -3y = 0
Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: Jx1, х2) %3D (Зхі — 5х2, —6х1 + 10x), K(x1, x2) = (-V3x2, 3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (Зх1 + 5х, бх1 — бх2), N(x1, x2) = (-v5x1, v5x2). (a) In each case, compute the determinant of the transformation. . det J= ,det K ,det L= ,det M= ,det N
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Please explain how you know the transformation is linear or not! Thank you! Which of the following transformations are linear? yi А. y2 X1X2 %3D В. y2 X3 %3D Y3 X1 %3D Yi 2x1 – 5x2 + 3x3 %3D С. y2 6x2 – 4x3 %3D Уз -10x1 – 8x2 yi 4 D. y2 8. = Уз 10 yi 4x1 + x2 'E. Y2 -X1 -3x1 = yi F. y2 5x1 %3D Уз 9x1 %3D I| ||||
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5. What is the standard matrix for the linear transformation given by a clockwise rotation by 45° followed by a reflection about the line y = -x.
1) Derive the matrix that performs the following consecutive transformations(in augmented form):1- Translation of 2 units along x-axis.2- Rotation by 90° about z-axis.3- Rotation by 90° about y-axis.
Which of the following transformations are linear? yi X] + 10 y2 X2 8x1 Yı 7 y2 3x1 + x2 C. -Xi 0. y2 D. 9x2 %3D y2 E.3 y2 Уз 3 X1 7x1 – 2x2 + 6x3 y2 = 10x2 - 3x3 -4x1 – 9x2 F.- Y3 = |L || || || I| || || || IL || || || A. B.
Write the matrix corresponding to the following linear transformations. Yı 2x1 – x2 – x3 Y2 3x3 Y3 = x1 + x2 2. -1 -1 3 1 1 2 -1 -1 3 1 2 -1 -1 1 1 1 2. -1 1 3 1 1 1
Suppose that vertices of a hut-shaped triangle on a computer screen are given by the coordinates (1, 0), (5, 0). (5, 3). (3, 5) & (1, 3). Transform this hut in following order 1. Reflect it along x-axis 2. Rotate it 180° counterclockwise i. Write 2*2 matrices for each transformation. Representing the above hut-shaped in form of data matrix, apply these transformations one by one and draw it at each step Find a single matrix of the composite transformation which performs both transformations at once. Apply it to the hut and draw it. It should be the same with the one obtained in part i. ii.
(c) Obtain the 3x3 transformation matrix that first scales a two-dimensional object by a factor of 2 in the x-direction and then reflects the modified object in the y-axis and finally translates the object by 4 in the x-direction and -3 in the y-direction.

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5. Determine the matrix of the transformation that first reflects points through the horizontal x-axis and then reflects points through the line y = x.