Suppose that T is a linear transformation such that 7 (8)-[:), -(1)-A- 5 Write T as a matrix transformation. For any i E R, the linear transformation T is given by T(x) x.

Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear transformation from R² to R² with associated matrix Determine the matrix C of the composition To S. C = -2 A = 4-633 1 B = 2 -3 [4] -2 -2

Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear transformation from R² to R² with associated matrix Determine the matrix C of the composition To S. C= 2 4-843 3]. A = B = 2 21.

Suppose T : R^2 → R^2 is a linear transformation that does not alter e_i andwhich maps e_2 into e_2 + 2e_1, where e_i = (1,0), e_2 = (0,1). Find the transformation matrix T.Justify your answer.