Math 018, Fall 2011
Quiz 2
Monday, September 19
Name:
Section (circle):
001
002
Show all work clearly, and circle your nal answers. You have 15 minutes to complete this quiz.
1.
(3 points ) The supply and demand for Penn State Math Club t-shirts is given
Math 018, Fall 2011
Quiz 3
Wednesday, October 5
Name:
Section (circle):
001
002
Show all work clearly, and circle your nal answers. You have 15 minutes to complete this quiz.
1. (7 points ) Farmer Phil needs to treat his garden with potash and nitrogen. H
Math 018, Fall 2011
Quiz 4
Wednesday, October 5
Name:
Section (circle):
001
002
Show all work clearly, and circle your nal answers. You have 15 minutes to complete this quiz.
1.
(2 points ) Finish the Gauss-Jordan method on the matrix:
132 3
0 1 0 2
0 0
Math 018, Fall 2011
Quiz 5
Wednesday, October 19
Name:
Section (circle):
001
002
Show all work clearly, and circle your nal answers. You have 15 minutes to complete this quiz.
1.
(4 points ) For each matrix, either nd its inverse or explain why it has no
MATH 018: Elementary Linear Algebra
Homework 10
Due Wednesday, November 16, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (2 points). Plot each linear inequality on its own set of axes:
(i) y > x + 3
(ii) x 4
Pro
MATH 018: Elementary Linear Algebra
Homework 9
Due Monday, November 7, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (5 points). Consider an economy of medical services and education. Each unit of medical service
MATH 018: Elementary Linear Algebra
Homework 11
Due Monday, December 5, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (4 Points). You are throwing a party and are providing soft drinks. You plan to buy two brands
MATH 018: Elementary Linear Algebra
Homework 12 (Sections 1.1-2.1 Review)
Due Monday, December 19
Please write your name and section number on all pages of your solutions.
Each of the following problems is worth 1 point. You MUST show all your work to rec
MATH 018: Elementary Linear Algebra
Homework 13 (Sections 2.2-2.6 Review)
Due Monday, December 12
Please write your name and section number on all pages of your solutions.
Each of the following problems is worth 1 point. You MUST show all your work to rec
MATH 018: Elementary Linear Algebra
Homework 8
Due Friday, November 4, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (5 points). The students of Pi Mu Epsilon are preparing for their annual bake sale. They plan t
MATH 018: Elementary Linear Algebra
Homework 7
Due Monday, October 24, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (3 points). Invert the matrices. If you cant, say why not:
A=
2
4
1
5
0
2
B=
4
3
2
1
Problem 2
MATH 018: Elementary Linear Algebra
Homework 3
Due Monday, September 19, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (5 points). A high school band is practicing a song for their big concert. The instructor has
MATH 018: Elementary Linear Algebra
Homework 2
Due Friday, September 9, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (2 points). Solve the following:
(i) Let f be the function given by f (x) = 2 x 1. Evaluate f
MATH 018: Elementary Linear Algebra
Homework 4
Due Monday, October 3, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (4 points). Solve the system with the echelon method. If there exists no solution, say so. If th
MATH 018: Elementary Linear Algebra
Homework 5
Due Monday, October 10, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (5 points). Solve the system with the Gauss-Jordan method. If no solution exists, say so. If
in
MATH 018: Elementary Linear Algebra
Homework 6
Due Monday, October 17, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (2 points). The following matrix M displays the approximate number of miles between certain cit
Math 018, Fall 2011
Quiz 1 - Solutions
Wednesday, September 7
1.
(3 points ) Find the equation of the line through the points (1, 5) and (2, 4) in slopeintercept form.
Solution. To nd the equation, we rst use the points (x1 , y1 ) = (1, 5) and (x2 , y2 )
1. Find the slope of the line through the 2 points pictured:
a) 2
b)
c)
3
2
2
3
d) 3
The 2 points above are (x1 , y1 ) = (2, 1) and (x2 , y2 ) = (1, 1). To nd the slope of the line passing through
them, we use the slope formula:
m=
1 (1)
2
y2 y1
=
=
x2 x1
Math 018
Exam II
1. The matrices below represent the augmented
matrix of a system of 3 linear equations with
3 variables x, y, z which has been row reduced.
As usual the rst column corresponds to x, the
second column corresponds to y , and the third
colum
Math 018
Exam II
1. Write the following system of equations as an
augmented matrix: (dont solve the system!)
7 + y = x 3 z
y + 2x + z + 1 = 0
x=z
2. Perform the row operation 2R1 3R2 R2 on
the following matrix: (dont solve the system!)
3 1 2 7
2
3 0 1
0 5
Math 018
Exam I
Sample C
1. Find an equation of the line through the points (1, 2) and (3, 4).
2. Sketch the graph of the line 2x y = 3.
3. Give an example (equation) of a line without a slope.
4. Determine whether the following pairs of lines are coincid
Math 018
Exam I
Sample B
1. Find an equation for the line through the points (1, 3) and (5, 5).
2. Find an equation for the line through the points (3, 5) and (3, 10).
3. Determine the equation of the line passing through the points (2, 1) and (3, 1) and
Math 018
Exam I
1. Find the slope of each of the following straight
lines:
(a) The line which passes through the points
(1, 3) and (5, 2).
(b) The line with equation 4x + 2y = 9.
(c) Any line perpendicular to the line with
3
equation y = 2 x + 5.
2. Circl
MATH 018: Elementary Linear Algebra
Homework 1
Solutions
Problem 1 (4 points). Lines A, B , and C are given. Find the slope of each, and indicate which of the lines (if
any) are parallel or perpendicular to each other.
A) The line given by 2x 4y = 14.
B)
MATH 018: Elementary Linear Algebra
Homework 2
Solutions
Problem 1 (2 points). Solve the following:
(i) Let f be the function given by f (x) = 2 x 1. Evaluate f at 3, 1, and 6.
3
(ii) Let L be the line below:
If L is the graph of a function g (x), nd a fo
MATH 018: Elementary Linear Algebra
Homework 2
Solutions
Problem 1 (5 points). A high school band is practicing a song for their big concert. The instructor has a student
take down 2 types of data: the number of measures passed in the song, and the number
MATH 018: Elementary Linear Algebra
Homework 4
Solutions
Problem 1 (4 points). Solve the system with the echelon method. If there exists no solution, say so. If there
are innitely many solutions, write the parameterized solution and give the solution when
MATH 018: Elementary Linear Algebra
Homework 5
Solutions
Problem 1 (5 points). Solve the system with the Gauss-Jordan method. If no solution exists, say so. If
innitely many solutions exist, nd the parameterized solution.
y z
2x 4y + 6z
x + 2y z
= 8
=
8
=
MATH 018: Elementary Linear Algebra
Homework 6
Due Monday, October 17, 2011
Please write your name and section number on all pages of your solutions.
Problem 1 (2 points). The following matrix M displays the approximate number of miles between certain cit