Let L : R → R³ be a linear transformation and the standard matrix representing L is 1 -2 -3 A = -1 2 1 What is the correct definition of the linear transformation L(v) = Av, where v = E R3? x2 x3 - 2x2 – 3x3 L -a1 + x3 x3 2x1 + x2 x1 – 3x2 – 2æ3 L 2x1 + x2 23 -xi + x3 - 2x2 – 3x3 L 2x1 + x2 -x1 + x3 - 3x2 – 2x3 L -a1 + x3 2x1 + x2

Let T be the linear transformation associated with the matrix: 0 1 -1 0 Find T(V) if V is the vector: 2 2 Is the transformation a rotation or a reflection? Justify why.

Determine the matrix of the linear transformation T(x, y) = (3x + 5y, 3y – 2x) 5 -2 3 (a) -2 3 (b) (c) 3 3 3 (d) 3 3 -2 a 2]

f and g are linear transformations which in matrix form are (0  -4) and (3  3)                           (2  1)         (-5  -4)  What is the image of the point (-1,1) under the composite transformation g o f?

Suppose that f : R² → R² is the linear transformation which first rotates a vector 90 degrees clock- wise and then multiplies the first coordinate by 2. Find a 2 × 2 matrix A such that f(x) = Ax for any vector x E R².