1.

^{x^2 , e^x, x^3, x^3+x , x^3-x , sin(x),}

^{For each of the equations that map R to R, choose the ones that are one-to-one.}

^2.

If B:C3 > C4, answer the following: a. Suppose solving Bu = 04 has one free variable, is B one-to-one and what is the dimension of the null space? b. Suppose solving Bu = 04 has two free variables, is B one-to-one and what is the dimension of the range? 0. Can B have no free variables and if so, what is the dimension of the null space? (1. Can B have four free variables, and if so, what is the dimension of the null space