Which of the following functions are linear transformations

Question

1. Which of the following functions are linear transformations?

(a) L: R₂ → R₃ define by

     L([u₁     u₂]) = [u₁   u₂    u₁ + u₂]

(b) L: R₂ → R₃ defined by

     L([u₁   u₂]) = [u₁ + u₂     u₂     u₂ - 1]

2. Find the standard matrix representing each given linear transformation.

(a) L: R² → R³ defined by L

	u1	0
L	u2	u1

(b) L: R² → R³ defined by

(c) L: R² → R³ defined by

3. Let L: R³ → R² be a linear transformation for which w know that

(a) What is L

     1
L  -2
     3

(b) What is L

     u₁
L   u2
     u₃