Math 280
Quiz 3
Spring 2014
Louiza Fouli
SOLUTIONS
1
3 4
5
2 .
1. (12 pts) Let A = 1
3 7 6
(a) Do the columns of A span R3 ? Justify your answer.
We must row reduce the matrix rst.
1
3 4 r2 r2 r1 1 3 4
1 3 4 r2 r2 /2 1 3 4
r3 r3 /12
r r3 +3r
r r3 r
1
5
2
Math 280
Quiz 5
Spring 2014
Louiza Fouli
SOLUTIONS
1
0 2
4 .
1. (8 pts) Find the inverse of the matrix A if it exists, where A = 3 1
2 3 4
Solution: We
1
0 2
3 1
4
2 3 4
r1 r1 +r3 1 0
r2 r2 +r3
0 1
0 0
Therefore A1
must row reduce the augmented matrix A I
Math 280
Quidelines For Review For Exam 1
Spring 2014
1. The exam will cover the sections 1.1-1.5, 1.7-1.9.
2. The exam will be in class on Tuesday, March 4th and NO notes, and NO calculators may be
used. There will be both computational problems and some
Math 280
Quidelines For Review For Exam 2
Spring 2014
1. The exam will cover the sections 2.1-2.3, 4.1-4.4.
2. The exam will be in class on Tuesday, April 22 and NO notes, and NO calculators may be used.
There will be both computational problems and some
Math 280
Exam 1-Solutions
Spring 2014
Louiza Fouli
SOLUTIONS
1. (10 pts)
(a) (5 pts) State carefully the denition for a set of vectors to be linearly independent.
A set of vectors cfw_v1 , . . . , vp in Rn are linearly independent if the only solutions t
Math 280
Quiz 2
Spring 2014
Louiza Fouli
SOLUTIONS
1. (10 pts) Let u=
2
2
h
and let v =
. Find the values of h, k so that b =
is in
1
1
k
Spancfw_ u, v .
Solution: Notice that b is in Spancfw_ u, v if and only if b is a linear combination of u
and v
Math 280
Exam 2
Spring 2014
Louiza Fouli
SOLUTIONS
1. (10 pts)
(a) (5 pts) State carefully the denition of a subspace of a vector space.
Let V be a vector space. A subset H of V is a subspace of V if the following three
conditions hold.
(a) 0 H.
(b) For
Math 280
Quiz 1
Spring 2014
Louiza Fouli
SOLUTIONS
1. (14 pts) Determine if the following system is consistent or inconsistent. You do not need
to solve the system completely. [Show ALL your work]
x1 + 2x2 + 3x3 = 8
3x1 + 4x2 + 5x3 = 9
5x1 + 6x2 + 7x3 = 1