MATH 2120: Quiz #3 SOLUTIONS
/6
Problem 1: Let A =
2 4
. Find A1 and use it to solve the following linear systems:
1 3
(a)
2x + 4y = 10
x + 3y = 2
A1 =
1
(2)(3) (4)(1)
2x + 4y = 1
x + 3y = 3
(b)
3 4
1
2
Ax = b = x = A1 b,
(a)
(b)
/4
2 4
1 3
x
=
y
x
10
=
y
Name:
Student #:
MATH 212
Linear Algebra I
Instructor: Richard Taylor
FINAL EXAM
24 April 2006
19:0022:00
Instructions:
1. Read all instructions carefully.
problem
grade
out of
2. Read the whole exam before beginning.
3. Make sure you have all 9 pages.
1
GRADE:
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Student #:
Okanagan University College
Salmon Arm Campus
MATH 221 Introduction to Linear Algebra
MIDTERM EXAM #1
2 March 2004
Instructor: Richard Taylor
Instructions:
1. Read all instructions carefully.
2. Read the whole exam before begin
MATH 2120 F14 Exam Review
1
Exam Review
The nal exam will cover the following sections from the textbook:
1.1-1.3
2.1-2.3, 2.4 (balancing equations, network analysis)
3.1- 3.3,3.5-3.6, 3.7 (Markov Chains, Population growth)
4.1-4.4, 4.6(steady state vecto
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MATH 2120 F14 Test 2 Solutions
1
(
( ) (
) (
)
)
x
2x
x
x
1. Let T1
=
and T2
=
. Let T be the transfory
y
y
x+y
mation from R2 to R2 obtained by rst applying T1 , and then T2 .
a) Find the matrix of the transformation T.
( ) (
( ) (
)( )
)( )
x
2 0
x
x
1
MATH 2120 F14 Quiz 6 Solutions
1
1. In a Markov chain, there are two states 0 and 1. When the system is in state 0, it
stays in that state with probability 0.4. When the system is in state 1, it transitions
to state 0 with probability 0.8.
a) Find the tra
MATH 2120 F14 Quiz 2 Solutions
1
1. Give the vector equation of the plane passing through the points P = (1, 0, 0), Q =
(0, 1, 0), and R = (0, 0, 1).
Solution Let
0
1
1
u = PQ = 1 0 = 1
0
0
0
0
1
1
v = PR = 0 0 = 0
1
0
1
x0
1
x
Let y0 = P = 0 .
MATH 2120 F14 Quiz 4 Solutions
1
1. Balance the following chemical reaction (photosynthesis):
CO2 + H2 O C6 H12 O6 + O2 .
#H
Solution For each compound in the reaction, associate a vector #C . Let
#O
x1 , x2 , x3 , x4 be the number of CO2 , H2 O, C6 H12 O
MATH 2120 F14 Quiz 1 Solutions
(
1. Given the vectors a =
2
3
1
)
(
and b =
2
1
)
, nd the vector x, given that x a +
2b = 2(x 2a).
Solution
x = 2x 4a
x = 3a + 2b ) (
(
) (
)
2
2
2
= 3
+
=
.
3
4
11
0
1
1 and v = 1 , nd the projection of u onto v.
2. Gi
Monthly Utility Expenses for 2016
$250
82.13
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$Jan
Feb
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Apr
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Electric
Jul
Gas
Water
Aug
Sep
Oct
Nov
Dec
Monthly Utility Expenses for 2016
$140
$120
115.85
115.49
$100
82.13
$80
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$Jan
Feb
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May
Jun
Name:
Student #:
GRADE:
/31
MATH 212
Linear Algebra I
Instructor: Richard Taylor
MIDTERM EXAM #1
17 February 2006 08:3009:20
Instructions:
1. Read all instructions carefully.
2. Read the whole exam before beginning.
3. Make sure you have all 6 pages.
4. O
MATH 212
Linear Algebra I
Instructor: Richard Taylor
FINAL EXAM
SOLUTIONS
19 April 2008
09:0012:00
problem
grade
out of
1
2
Instructions:
1. Read all instructions carefully.
2. Read the whole exam before beginning.
3. Make sure you have all 8 pages.
4. Or
Name:
Student #:
GRADE:
/50
Okanagan University College
Department of Mathematics & Statistics
MATH 221 Introduction to Linear Algebra
FINAL EXAM
22 April 2005 09:0012:00
Salmon Arm Campus
Instructor: Richard Taylor
Instructions:
Read all instructions ca
MATH 2120: Quiz #6 SOLUTIONS
/10
Problem 1: Let TA (x) be a linear transformation of the (x, y)-plane that performs a reection across
the line y = x followed by a clockwise rotation by 45 .
(a) Find the matrix A such that TA (x) = Ax.
Write
TA (x) = A2 A1
Name:
Student #:
MATH 2120
Linear Algebra I
Instructor: Richard Taylor
FINAL EXAM #1 (IN-CLASS COMPONENT)
10 April 2014 11:3012:45
problem
grade
out of
1
9
Instructions:
2
5
1. Read the whole exam before beginning.
3
4
2. Make sure you have all 5 pages.
3
MATH 212 Linear Algebra I
Richard Taylor Thompson Rivers University
last revision: January 16, 2008
1
Systems of Linear Equations
Lec. #1
In your other courses you might have already met with a problem similar to the following.
Example 1.1. Find numbers x
MATH 2120: Quiz #1 SOLUTIONS
/5
Problem 1: Use Gauss-Jordan elimination to solve the following system of linear equations.
x + 3y + z = 7
3x + 9y + 7z = 6
1 3 1 7
3 9 7 6
R 3R
2 1
x = 43 3y
4
= y is free
z = 15
4
/5
1 3 1
7
0 0 4 15
x = 43 3t
4
=
y=t
z
MATH 2120
Linear Algebra I
Instructor: Richard Taylor
MIDTERM EXAM #2
SOLUTIONS
20 March 2014 11:3012:45
problem
Instructions:
1. Read the whole exam before beginning.
2. Make sure you have all 5 pages.
3. Organization and neatness count.
4. Justify your
MATH 2120: Quiz #5 SOLUTIONS
/5
Problem 1: Let V R3 be the set of vectors of the form (a, b, c) where b = a + c. Is V a subspace of
R3 ? If so, nd a basis for V .
To show closure under scalar multiplication:
v1
ta
a
Let x = a + c V . For any t R we have
MATH 2120 Final Exam #2 (take-home component)
11 April 2014
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Signature:
Instructions:
1. Prepare your solutions on your own paper, stapled with this exam paper at the front.
2. It is permissible to discuss the problems with other students or faculty
MATH 2120
Linear Algebra I
Instructor: Richard Taylor
MIDTERM EXAM #1
SOLUTIONS
6 February 2014
11:3012:45
problem
grade
out of
Instructions:
1
10
1. Read the whole exam before beginning.
2. Make sure you have all 4 pages.
2
10
3
10
3. Organization and ne
GRADE:
Name:
/42
Student #:
Okanagan University College
Salmon Arm Campus
MATH 221 Introduction to Linear Algebra
MIDTERM EXAM #2
25 March 2004
Instructor: Richard Taylor
Instructions:
1. Read all instructions carefully.
2. Read the whole exam before begi