Math 571
Winter 2008
Quiz 4
Instructions: This quiz is worth a total of 10 points, and the value of each question is listed with each
question. You may use any notes or books but you must work individually. The only computation aid
which you may use is MA
Math 571
Winter 2008
Project 2
Instructions: This project is worth a total of 10 points. You may use any notes or books that you
wish but you must work individually. The only computation aid which you may use is MATLAB, unless
otherwise indicated. The pri
Math 571
Winter 2008
Project 2 Solutions
0.35
(1a.) M = 0.35
0.30
0.50
0.25
0.25
0.15
0.55
0.30
91
90.765
120
(b.) M 5 80 = 96.036 which rounds to 96.
73
73.198
60
(c.) Find a basis vector x for N (M I ) using the MATLAB command x=null(M-eye(3). This
give
Math 571
Winter 2008
Project 1
Instructions: This project is worth a total of 10 points. You may use any notes or books that you
wish but you must work individually. The only computation aid which you may use is MATLAB,
unless otherwise indicated. The pri
Math 571
Winter 2008
Project 3
Instructions: This project is worth a total of 10 points. You may use any notes or books that you wish
but you must work individually. The only computation aid which you may use is MATLAB, unless otherwise indicated. The pri
Math 571
Winter 2008
Project 4
Instructions: This project is worth a total of 10 points. You may use any notes or books that you
wish but you must work individually. The only computation aid which you may use is MATLAB, unless
otherwise indicated. The pri
Math 571
Winter 2008
Quiz 3
Instructions: This quiz is worth a total of 10 points, and the value of each question is listed with each
question. You may use any notes or books but you must work individually. The only computation aid
which you may use is MA
Math 571
Winter 2008
Solutions to Quiz 5
(1a.) Just verify the three axioms hold.
(bi.) x, y = xt A y = 29,
(ii.) |x| =
(iii.) p =
xt A x =
xt Ay
y t A y
3
1
yt A y =
22 and |y| =
49,
29
49 y
xt Ay
|x|y|
(iv.) = cos1
y =
= 0.4880 radians.
2
1
. Then S = C
Math 571
Winter 2008
Quiz 6
Instructions: This quiz is worth 10 points and the value of of each question is listed with each question.
You may use any notes or books but you must work individually. The only computation aid which you
may use is MATLAB, unl
Some Notes on the Final Exam
Math 571
Winter 2008
(1.) Know how to solve a system of linear equations.
(a.) How to form the augmented matrix.
(b.) How to row reduce by hand.
(c.) How to use MATLAB to row reduce.
(d.) Understand the number of solutions tha
Math 571
Winter 2008
Quiz 1
Instructions: This quiz is worth a total of 10 points. You may use any notes or books but you
must work individually. The only computation aid which you may use is MATLAB, unless otherwise
indicated. Make sure to write clearly
Math 571
Winter 2008
Quiz 2
Instructions: This quiz is worth a total of 10 points. You may use any notes or books but you
must work individually. The only computation aid which you may use is MATLAB, unless otherwise
indicated. Make sure to write clearly
Math 571
Winter 2008
Solutions to Quiz 3
2x2 x3
(1a.) YES: A typical vector is: x2
x3
00
(o.) 0 = 0 is in S .
0
2y 2 y 3
2x2 x3 + 2y2 y3
2(x2 + y2 ) (x3 + y3 )
=
, so the sum
(i.) x2 + y2 =
x2 + y2
x2 + y2
x3
y3
x3 + y3
x3 + y3
of any two vectors in S r
Math 571
Winter 2008
Solutions to Quiz 4
10
3 3 2 and row reduce to 0 1
(1a.) Form A =
00
12 1 19
non-pivot column, these vectors are linearly DEPENDENT.
9
3
12
1.6667
0.5 . Since the third column is a
0
(1b.) Consider the equation:
1 (x2 3) + 2 (x 2) +
Math 571
Winter 2008
Quiz 5
Instructions: This quiz is worth 10 points and the value of of each question is listed with each question.
You may use any notes or books but you must work individually. The only computation aid which you may
use is MATLAB, unl
Math 571
Winter 2008
Solutions to Project 4
2
145
1
1
3 7 10 1
and b = 3
2 3 5
(1.) Let A =
2
5 6 11 1
1
1
123
0
Note rank(A) = 3 so AT A is not invertible, so we must solve for x by row reducing AT A | AT b :
1
0
1
0
0
AT A | AT b
0
0
1
1
0
0
0