Which of the following is not alinear transformation?Select all possible answers.T (x, y) = (2x + 3, 4y)OT (u, v) = (u, u)The transformation given by the matrix(: :)1 0T =1

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Answered: Which of the following is not a linear…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

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Similar questions

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}.
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 T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
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.
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
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrix

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Which of the following is not a linear transformation? Select all possible answers. T (x, y) = (2x + 3, 4y) T(и, 0) — (и, и) The transformation given by the matrix 1 T 1