Topic is Linear Transformation: Instruction: Provide the image for v and the pre-image for u of the given linear transformation: a. T: R 2 -> R 2, T(v 1 ,v 2 ) = (v 1 , v 1 + 2v 2 ) , where v = (2,3),...

Topic is Linear Transformation:

Instruction: Provide the image for v and the pre-image for u of the given linear transformation:

a. T: R₂
-> R_2,
T(v₁
,v₂) = (v₁
, v₁
+ 2v₂) , where v = (2,3), u = (4,12)

b. T: R₃
-> R_3,
T(v1 , v2 , v₃
) = (0 , v₁
+ v₂
, v₂+ v₃) , v = (-3,2,5) , u = (0,2,5)