Problem 9. Find the standard matrix of the linear transformation T: R2 R2 that reflects a vectorthrough the origin.

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Answered: Problem 9. Find the standard matrix of…

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 7CM: In Exercises 7-10, find the standard matrix for the linear transformation T. T(x,y)=(3x+2y,2yx)

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Here is a data matrix for a line drawing: D=[012100002440] aDraw the image represented by D. bLet T=[1101]. Calculate the matrix product TD, and draw the image represented by this product. What is the effect of the transformation T? cExpress T as a product of a shear matrix and a reflection matrix. See Problem 2. 2. Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c=3 in the expansion matrix and c=1 in the shear matrix. T1=[1001] Reflection in yaxis T2=[100c] Expansion or contraction in ydirection T3=[10c1] Shear in ydirection
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?
In Exercises 7-10, find the standard matrix for the linear transformation T. T(x,y)=(3x+2y,2yx)
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Problem 9. Find the standard matrix of the linear transformation T: R2 R2 that reflects a vector through the origin.