Determine whether the function is a linear transformation. T: R2 → R³, T(x, y) = (2x², 3xy, y²) O linear transformation O not a linear transformation

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).

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.

Linear TransformationsIn Exercises 9-22, determine whether the function is a linear transformation. T:33, T(x,y,z)=(x+y,xy,z)