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The linear transformation is such that for any v in R2, T(v) = Av. a) Use this...

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Advance Math

The linear transformation is such that for any v inR2, T(v) = Av.

a) Use this relation to find the image of the vectorsv1 = [-3,2]T and v2 =[2,3]T. For the following transformations take k = 0.5first then k = 3,

T1(x,y) = (kx,y)

T2(x,y) = (x,ky)

T3(x,y) = (x+ky,y)

T4(x,y) = (x,kx+y)

For T5 take theta = (pi/4) and then theta =(pi/2)

T5(x,y) = (cos(theta)x - sin(theta)y, sin(theta)x +cos(theta)y)

b) Plot v1 and v2 and their images underthe transformations. Write a short description saying what thetransformations is doing to the vectors.

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