Let T: R² →R² be a linear transformation that maps u = 3 5 2 -1 into and maps v = into - [ ] [ ³ ] [ 2 ] 4 2 fact that T is linear to find the images under T of 3u, 2v, and 3u + 2v. The image of 3u is Use the

Please show work

Let Tv = Av represent the linear transformation T: R2 → R3 where 1 2 A = -2 4 -2 2]

Topic is Linear Transformation: Instruction: Provide the image for v and the pre-image for u of the given linear transformation: a. T: R2 -> R2, T(v1 ,v2) = (v1 , v1 + 2v2) , where v = (2,3), u = (4,12) b. T: R3 -> R3,  T(v1 , v2 , v3 ) = (0 , v1 + v2 , v2 + v3) , v = (-3,2,5) , u = (0,2,5)