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 individ
Math 571
Winter 2008
Project 1 Solutions
(1a.) The voxels that the beams pass through are listed in the following table:
0 deg.
45 deg. 90 deg.
135 deg.
Beam 1
1,2,3
1,2,4
1,4,7
4,7,8
Beam 2
4,5,6
3,5
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
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
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
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
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
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 individ
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
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. Th
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
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,
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,
Math 571
Winter 2008
Solutions to Quiz 1
14 4
27
(1a.) A = 5
42
3
10
40
41
5
5
14
4
27
(b.) Put A into echelon form U = 0
0
4
1
41
0
+5
60
(bi.) No Solution: = 5 and = 60
(bii.) A Unique Solution: =
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 i
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. Th
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 redu