Linear algebra  basis multiple choice questions
Play with examples. For #4, use U=the plane, V=the plane, and B={i,j} (the standard basis). Can you give an example of T that isn't onetoone? Now test each of the five responses with this T. I bet you can rule out four of them.
For #5, write down an actual cubic, and then find Dx of your cubic. Try another one. Pretty soon, you'll find that one of the five responses is obviously correct (and hopefully the other four are therefore wrong).
