 Can a set of vectors that includes the 0 vector be linearly independent?
a) Yes and I can give an example
b) Yes but I am unsure of why
c) No but I am unsure of why not
d) No and I can explain why not
 Can a matrix span R^{3}?
a) Yes and I can give an example
b) Yes but I am unsure of why
c) No but I am unsure of why not
d) No and I can explain why not
 The columns of a 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
 If vectors are not linearly independent then they can't span R^{2}
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
 Let z be any vector from R^{3}:
If we have a given set V of vectors from R^{3}; how
many vectors must be in V to guarantee that z can be written as a linear
combination of the vectors in V ?
a) 2
b) 3
c) 4
d) It is not possible to make such a guarantee
 How would we geometrically
describe the span of (1,0,0), (0,0,1) and (1,2,3)?
a) A point
b) A line segment
c) A line
d) R^{2}
e) R^{3}

If two vectors are linearly independent, they must be
perpendicular (orthogonal).
(a) True, and I am very confident
(b) True, but I am not very confident
(c) False, but I am not very confident
(d) False, and I am very confident
 Which set of vectors is linearly independent?
(a) (2, 3), (8, 12)
(b) (1, 2, 3), (4, 5, 6), (7, 8, 9)
(c) (3,1,0), (4, 5, 2), (1, 6, 2)
(d) None of these sets are linearly independent.
(e) Exactly two of these sets are linearly independent.
 Lucinda owns two ice cream parlors.
The first ice cream shop sells 5 gallons of vanilla
ice cream and 8 gallons of chocolate ice cream each day. The daily sales at
the second
store are 6 gallons of vanilla ice cream and 10 gallons of chocolate ice
cream. The
daily sales at stores one and two can be represented by the vectors s1 =
(5,8) and
s2 = (6,10) respectively.
In this context, what interpretation can be given to the
vector 15s1?
(a) 15s1 shows the number of people that can be served with 15 gallons of vanilla ice
cream.
(b) 15s1 shows the gallons of vanilla and chocolate ice cream sold by store 1 in 15
days.
(c) 15s1 gives the total revenue from selling 15 gallons of ice cream at store 1.
(d) 15s1 represents the number of days it will take to sell 15 gallons of ice cream at
store 1.
 The stores are run by different managers, and they are not
always able to be open the same number of days in a month. If store 1 is open
for
c1 days in March, and store 2 is open for c2 days in March, which of the following
represents the total sales of each
flavor of ice cream between the two stores?
a) c1s1+c2s2
b) Matrix([[5,6],[8,10]]).Vector([c1,c2])
c) Vector([5c1,8c1]) + Vector([6c2,10c2])
d) All of the above
e) None of the above
 Lucinda is getting ready to close her ice cream parlors for
the winter. She has a total of 39 gallons of vanilla ice cream in her
warehouse, and 64
gallons of chocolate ice cream. She would like to distribute the ice cream to
the two
stores so that it is used up before the stores close for the winter. How
much ice cream
should she take to each store? The stores may stay open for different number
of days,
but no store may run out of ice cream before the end of the day on which it
closes.
a) 3 gallons of each kind to store 1 and 4 gallons of each kind to store 2
b) 3 gallons of vanilla to each store and 4 gallons of chocolate to
each store
c) 15 gallons of vanilla and 24 gallons of chocolate to store 1 and
24 gallons of vanilla and 40 gallons of chocolate to store 2
d) This cannot be done unless ice cream is thrown out or a store runs
out of ice cream before the end of the day

For full credit, which of the following are true regarding graded problem sets
a) I must print out all work, including Maple ReducedRowEchelonForm
commands and output
b) I must annotate/explain my
methods and reasoning with handwritten comments and/or typed comments.
c) both a) and b)
d) neither a) nor b)