Question

4. (a) Define what it means for a function T:R" → R to be a linear transformation. [2 marks] 4. (b) Let T:R2 + R2 be defined by T Show that T is not a linear transformation. (4 marks) 4. (c) Let A = 21. and T : R2 + Rº be the linear transformation defined by T'(x) = Ax for every x € R2 Sketch, as accurately as possible, a graph of the image under T of the square with vertices (0,0), (1.0), (1,1),(0,1). [4 marks]