1. In the hw from 1.4, in #13, the problem asked whether u was in the plane spanned by the columns of A. The answer is...
a) yes and I have a good reason why
b) yes but I am not sure why
c) no but I am not sure why not
d) no and I have a good reason why not
e) what's a "span"?

2. In Problem Set 1 number 1, the set of solutions is
a) a point
b) a line
c) does not exist
d) a hyperplane
e) non-linear

3. A linear-system has how many solutions:
a) 0 or 1
b) 0 or infinite
c) 0, 1 or infinite
d) 0, 1, 2 or infinite
e) none of the above

4. A homogeneous linear-system has how many solutions:
a) 0 or 1
b) 0 or infinite
c) 0, 1 or infinite
d) 0, 1, 2 or infinite
e) none of the above

5. Vector([1,1]) and Vector([2,2]) span
a) a point
b) a line
c) a plane
d) a hyperplane
e) non-linear

6. The columns of an n x m coefficient matrix span Rn exactly when the augmented matrix reduces to one with a pivot for each column except the equals column
a) True and I can explain why
b) True but I am unsure of why
c) False but I am unsure of why not
d) False and I can give a counterexample

7. To check whether a vector is in the span of other vectors, it suffices to see if they are multiples
a) True and I can explain why
b) True but I am unsure of why
c) False but I am unsure of why not
d) False and I can give a counterexample

8. If a collection of vectors is not l.i. then we could throw away any one vector and still span the same space
a) True and I can explain why
b) True but I am unsure of why
c) False but I am unsure of why not
d) False and I can give a counterexample

9. Which set of vectors is linearly independent?
(a) Vector([0, 0])
(b) Vector([1, 2, 3]), Vector([4, 5, 6]), Vector([7, 8, 9])
(c) Vector([-3,1,0]), Vector([4, 5, 2]), Vector([1, 6, 2])
(d) None of these sets are linearly independent.
(e) Exactly two of these sets are linearly independent.

10. LaTeX question on parametrization

Solutions
1. a)
3. c)
4. e) [1 or infinite as 0 vector always works]
5. b)
6. d)
7. d)
8. d)
9. d)
10.b)