(1) Give an example of 3 vector spaces that are not Rn. Explicitly state the definition of addition and the zero vector in each space.
(2) Let X1, . . . , Xk be linearly independent vectors in Rn, and let A be a nonsingular n × n matrix. Define Yi = AXi for i = 1, . . . , k. Show that Y1, . . . , Yk are linearly independent.