- 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"?

- 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

- 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

- 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

- Vector([1,1]) and Vector([2,2]) span

a) a point

b) a line

c) a plane

d) a hyperplane

e) non-linear

- The columns of an
*n*x*m*coefficient matrix span R^{n}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

- 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

- 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

- 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.

- 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)