Which of the following transformations are linear?A.Yı=8x2Y2=-6x3Y3=-3x1Yı=-9x1С.B.Y2=7x1Y3=6x1Y1=x1 + 5D.Y2=x2Y1=0O E.Y1=4x1+ 12O F.Y2=-I1 UpNextFind the matrix A of the linear transformation T from p2 to p2 that rotates any vector through an angle of 30° in the counterclockwise direction.INOTE: if you answer use cos(...) and sin(..), webwork expects the arguments to be in RADIANS.]Problems1A =2n3n 4Note: VoLcon ear nartielcnadit on thie poblemCLWARNIIAY 7:36WD00F9F10F880,F6F7F3F4F5&$467YU

Answered: Image /qna-images/answer/426343c1-dcd0-4bd5-ab6a-a9cddb1d4ee8.jpg

Answered: Which of the following transformations…

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 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

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Similar questions

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).
Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.
Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
For the linear transformation T:R2R2 given by A=[abba] find a and b such that T(12,5)=(13,0).
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .
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?
Let TA: 23 be the matrix transformation corresponding to A=[311124]. Find TA(u) and TA(v), where u=[12] v=[32].

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Which of the following transformations are linear? Yı=x} A. Yı=8r2 Y2=-6.x3 Y3=-3r1 Y1=-9r1 C. Y2=7x1 Y3=6x1 Y1=x1+ 5 D. Y2=x2 Y1=0 O E. Y1=4x1+ 12 O F. Y2=-T1