Given the linear transformation T with T(x1,x2) = (3x1 - 2x2, x1 + 4x2, x2). find its standard matrix, that is the unique matrix A with the property that T(x) = Ax for all x. (Note that x1, x2 are entries of x.) Let T: R2 rightarrow R3 be a linear transformation with T(x1,x2) = (2x1 - x2, -3x1 + x2, 2x1 - 3x2). Is (0,-1,-4)in range of T? If yes, find and x such that T(x) = (0,-1,-4).
