Practice Problems for Mid-Term 1 (261) (1) In each situation determine whether a and b are Never, Sometimes, or Always orthogonal: Give reasons/ example, algebraic and /or geometric.
U and V U and v
2
(a) (b) (c)
;
a= proju(v) b= v-proju(v) n ; a=
HW3: DETERMINANTS
Complete the assignment on separate paper, and turn in by the beginning of next
class (Thursday, 13 November). Simplify all answers without rounding. Show your
work neatly and box or circle your answer. Total: 10 points.
1. [0.5 pt each]
HW6: FINAL PRACTICE PROBLEMS
All answers must be exact and simplied.
Turn in on a separate paper at the beginning of the nal exam.
This is not a complete representation of what will be on the test; consult the
suggested HW and the study guide for more. Th
Name:
MTH261, MIDTERM
No calculators with matrix capabilities. Simplify all answers without rounding.
Show your work neatly and box or circle your answer.
Total: 5 pages, 90 points (15 of which are extra credit).
1.
[10 pt]
Balance the equation for photos
MTH261 MIDTERM STUDY GUIDE
The midterm covers the following sections: 1.1-1.5, 1.7-1.9, 2.1-2.3, 2.8, 2.9.
listed below. This guide is a
summary,
Things you are expected know are
and therefore does not include absolutely everything you need to know.
The o
Name / nombre / nume / pangalan / tn /
(
% add your language if it's not already there)
:
KEY
:
@
MTH261, QUIZ 1
No calculators. Simplify all answers without rounding. Show your work neatly and
box or circle your answer. Total: 2 pages, 10 points.
1.
~
[5
Name:
MTH261, QUIZ 2
No calculators. Simplify all answers without rounding. Show your work neatly and
box or circle your answer. Total: 2 pages, 10 points.
1. [2 pt] Let M be a h w matrix of constants, ~x be a w 1 vector of variables, and ~0 be the h 1 ze
Name:
MTH261, QUIZ 3
No calculators. Simplify all answers without rounding. Show your work neatly and
box or circle your answer. Total: 2 pages, 11 points (1 of which is extra credit).
44
0 0
2.9 0
0 1
1 0
1. Suppose we have
two
0
0
AB = 3I4 +
0
(a)
[1
Name:
MTH261, QUIZ 4
No calculators. Simplify all answers without rounding. Show your work neatly and
box or circle your answer. Total: 1 page, 10 points.
1.
[6 pt] Consider
A=
(a)
2
3
0
5
6
[6 pt]
matrix
A
0
2 2
3
3
e
3 3
0 1/6
0 0
1
10 2 1
1
k
0 8
Calcu
Name:
MTH261, QUIZ 5
No calculators. Simplify all answers without rounding. Show your work neatly and
box or circle your answer. Total: 2 pages, 10 points.
1. Let's
diagonalise
the matrix A, given below, if possible. (Note that A is the same for the ent
HW5: PSU cross-product worksheet (2 points each)
1.
2.
k
~0
k
k
~0
k
~0
~u
is parallel to
Or:
~v = 0 |~u ~v | = |~u| |~v | sin = |~u| |~v | (0) = 0 ~u ~v = ~0
k
~u is parallel to ~v ~v = c~u for some c R ~u ~v = ~u c~u = c(~u ~u) = u1 u2 u3
u1 u2 u3
HW2: CHEMISTRY, TRAFFIC, CIRCUITS, & MIGRATION
Complete the assignment on separate paper, and turn in by 5pm on Halloween.
Turn it in either in class, or in the MTH department oce (NH334, request to put
it in Eva Vanderzee's mailbox).
Simplify all answers
MTH 261 MIDTERM PRACTICE PROBLEMS
This is completely optional and only provided to help you study.
This is not a complete representation of what will be on the test; consult the
suggested HW and the study guide for more. This is also not an accurate
repre
I
"'
Qmz 1:
JANUARY
NAME:
10, 2014
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 ( 4
QUIZ
2:
JANUARY
NAME:
15, 2014
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 (4 poin
QUIZ
3:
JANUARY
22, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 (5 poin
QUIZ
4:
5, 2014
FEBRUARY
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 (4 poin
Qmz
5: FEBRUARY 14, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 ( 5 poi
Qmz 6:
FEBRUARY
19, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Let T : 1R2 ~ .IR
Qmz 7:
MARCH
5, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 (7 points):
QUIZ 8: MARCH 12, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 (6 points
EXAM
1:
JANUARY
27, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Problem 1 (8 poin
EXAM
2:
FEBRUARY
26, 2014
NAME:
As always, your answer will be graded on the quality of presentation as well as the correct
answer. To get a good score: write your answer clearly, in an orderly fashion, using words,
and showing your work.
Complete the sen
Here are some different ways to compute the condition number of a matrix. You want to
do this, because it tells you how close to singular your matrix is.
Matlab
According to OIT, this software is available in all the campus computer labs (except
Urban Cen
Carlos Cantos
ROTATION MATRIX
The matrix which rotates a 2D vector by
A=
sin
cos
cos
sin
radians counterclockwise is:
But where does this come from? The book has a nice picture on page 72, and looking at this picture everything
should seem correct, b
Name:
MTH261, QUIZ 6
No calculators. Simplify all answers without rounding. Show your work neatly and
box or circle your answer. Total: 2 pages, 10.5 points (0.5 of which is extra credit).
1. Let ~u and ~v be vectors in R3 , and be the angle between them.