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)