Math 322 - Matrix Algebra
Friday, September 19
S OLUTIONS
Quiz 3
Name:
1. (3 points) State what it means for the vectors u, v, and w in R5 to be linearly independent.
The vectors are linearly independent if the only solution to
x1 u + x2 v + x3 w = 0
is t
S OLUTIONS
Math 322 - Matrix Algebra
Friday, October 17
Quiz 6
Name:
1. (4 points) Use the determinants to nd the area of the parallelogram with vertices
1
,
1
4
,
5
2
,
7
5
.
1
and
None of the vertices are at the origin, so we rst translate the shape by
S OLUTIONS
Quiz 10
Math 322 - Matrix Algebra
Friday, November 21
Name:
1
2
1
3 , v = 4, and w = 1. Find the following quantities
1. (1 point each) Let u =
2
1
2
(a)
uv =
(b)
uw =
12
(c)
0
vw =
(d)
u =
8
14
1
3 perpendicular to .
2. (3 points) Find
Math 322 - Matrix Algebra
S OLUTIONS
Friday, December 5
Quiz 11
Name:
1
1
1 , 1 and let W = Span B . Find p, the orthogonal projec1. (4 points) Let B =
2
1
1
2 onto W and also nd the B -coordinates of p.
tion of b =
1
We write u1 and u2 for the vec
Math 322 - Matrix Algebra
Friday, October 24
Quiz 7
S OLUTIONS
Name:
1 2 3
1. (4 points) Find a basis for the null space and the column space of A = 1 4 6.
1 0 0
1 2 3
1 2 3
1 0 0
A 0 2 3 0 2 3 0 2 3
0 2 3
0 0 0
0 0 0
There are two pivots and one fre
Math 322 - Matrix Algebra
Friday, September 12
S OLUTIONS
Quiz 2
Name:
1. True/False. No justication required.
(a) If u and v are vectors in R3 , then Spancfw_u, v is always
a plane through the origin.
The span could also be a line or just a point.
T
/
F
Math 322 - Matrix Algebra
Friday, September 26
S OLUTIONS
Quiz 4
Name:
1. (4 points) Suppose that
4 1
1 2 3
A=
and
B = 2 2 .
2 0 5
3 1
Find the matrix products AB and BA, if they are dened. If either is not dened, simply
write NOT DEFINED.
Both products a
Name:
Date: 23 April 2009
QUIZ 8
1. Find the coordinate vector [x]B of x relative to the given basis B = cfw_b1 , b2 , b3 where:
8
1
3
2
9 , b1 = 1 , b2 = 4 , b3 = 2
x=
6
3
9
4
Solution: We need weights c1 , c2 , c3 where x =
ci bi . So we are solving th
MA 322 - Matrix Algebra
Exam 3
16 April 2009
Name:
Score:
/100 Points
Instructions:
You may not use any outside assistance on this exam. You may not use books,
notebooks, other peoples exams, or any other materials to cheat on this exam.
You may not use
MA 322 - Matrix Algebra
Exam 2
12 March 2009
Name:
Score:
/100 Points
Instructions:
You may not use any outside assistance on this exam. You may not use books,
notebooks, other peoples exams, or any other materials to cheat on this exam.
You may not use
MA 322 - Matrix Algebra
Exam 1
12 February 2009
Name:
Score:
/100 Points
Instructions:
You may not use any outside assistance on this exam. You may not use books,
notebooks, other peoples exams, or any other materials to cheat on this exam.
You may not
Name:
Date: 2 February 2008
QUIZ 2
1. (5 points) Complete Theorem 4 of section 1.4.
Let A be an m n matrix. Then the following statements are logically equivalent.
a) For each b Rm , the equation Ax = b has a solution
b) Each b Rm is a linear combination
Name:
Date: 19 February 2009
QUIZ 3
Consider the matrix:
1
0 2
4 .
A = 3 1
2 3 4
1. (5 points) Determine A1 using the algorithm described in section 2.2. (Hint: First
form the matrix [A I ].)
Forming the matrix requested we see:
1
0 2 1 0 0
4 0 1 0
[A I ]
Name:
Date: 9 April 2009
QUIZ 7
1. Consider the vectors below.
1
1
1
u 1 = 1 , u 2 = 1 , y = 4
0
0
3
(a) (3 points) Verify that the set cfw_u1, u2 is an orthogonal set.
Solution: Computing the dot product we see:
u1 u2 = (1)(1) + (1)(1) + (0)(0) = 0.
As
Name:
Date: 2 April 2009
QUIZ 6
1. Find a unit vector in the direction given by v =
30
.
40
Solution: To normalize v we divide by its magnitude to gain a unit vector u in the
direction of v .
|v | =
vv
=
900 + 1600
=
2500
= 50
Therefore a unit vector in t
Name:
Date: 26 February 2009
QUIZ 4
Consider the matrix:
4 5 9 2
1 2 6 5
A = 6 5 1 12 0 1 5 6
3 4 8 3
000 0
1. (4 points) Find a basis for Col A.
We know that the pivot columns of a matrix form a basis for its column space. The
pivot columns of A are the