Which of the following transformations are linear transforma

Which of the following transformations are linear transformations?

Which of the following transformations are linear transformations? (a) T(x,y) = (3-y, x, 2x+y) (e) T(x,y,z) = (0, 1) (b) T(x, y) = (x2, 2y) (f) T(x, y, z) = (y, 0, z) (c) T(x, y) = (y, x, x) (g) T(x, y, z) = (3xy, x + 2y, 3x - z) (d) T(x,y) = (0, 0, 0) (h) T(x,y,z) = (5x - 7y, 2x+z, 3)

Solution

(a) , (c) , (d) , (f) are all linear transformation.