Exercise 10.1.1 Consider the following functions T: R³ → R². For each of these functions T, show that it is not linear either by showing that T does not preserve addition, or by showing that it does not preserve scalar multiplication, or by showing that it does not preserve the zero vector. (a) T X y 7 X (b) T y Z (c) T x+2y+3z +1 2y-3x+z x+2y² +3z 2y+3x+z 8-1 y 7 sinx+2y+3z 2y+3x+z

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