Systems of Two Equations in Two Variables
MATH 107: Finite Mathematics
University of Louisville
January 8, 2014
6
Introduction
Denitions
2 / 25
What is a system of linear equations?
A linear equation in two variables is an equation of the form
ax + by = c
MATH 10701
Quiz #1 solutions
1. (7 points) A fruit grower uses two brands of fertilizer. Each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid, while each bag of brand B contains 7 pounds of nitrogen and 6 pounds of phosphoric
MATH 10701 Show all work.
Quiz #1
Name:
1. (7 points) A fruit grower uses two brands of fertilizer. Each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid, while each bag of brand B contains 7 pounds of nitrogen and 6 pounds of
MATH 10701
Practice Exam #1
Name:
Show all work.
1. (20 points) Two models of guitar are being produced by a factory. Model A has a labor cost
of $30 and a material cost of $20, while Model B has a labor cost of $40 and a material cost of
$30. Over the co
Systems of Linear Equations and Matrices
MATH 107: Finite Mathematics
University of Louisville
January 13, 2013
Introduction
Matrix terminology
2 / 12
Matrices
A matrix is a rectangle of numbers enclosed by square brackets.
A matrix is of size m n if it h
Row-reduction and Gauss-Jordan Elimination
MATH 107: Finite Mathematics
University of Louisville
January 15, 2014
Introduction
Reduced form
2 / 10
Desired matrix forms
We saw previously that every 2
3
augmented matrix is
row-equivalent to one of the three
MATH 10701 Show all work.
Quiz #2
Name:
1. (8 points) For each of the following matrices, either state that the given matrix is in reduced form or explain why it is not and indicate which row operation would transform it into reduced form. 1 0 2 3 0 0. (a
MATH 10701
Quiz #2 solutions
1. (8 points) For each of the following matrices, either state that the given matrix is in reduced form or explain why it is not and indicate which row operation would transform it into reduced form. 1 0 2 3 0 0. (a) (4 points
MATH 10701 Show all work.
Quiz #5
Name:
1. (7 points) Formulate a linear programming problem describing the following question. You do not need to solve the problem. Clearly label what each of your variables represents, and identify the constraints and an
MATH 10701
Quiz #5 solutions
1. (7 points) Formulate a linear programming problem describing the following question. Clearly label what each of your variables represents, and identify the constraints and an objective function. You are renting buses and va
MATH 10701 Show all work.
Quiz #3
Name:
1. (10 points) Either calculate the result of each arithmetic operation, or explain why it cannot be performed. (a) -3 1 2 5
2
(b)
3 -2 2 -1 3 -3 1 0 -1 - 2 0 4 -2 2 5 1 2
2. (3 points) Test to see if
5 -7 3 7 and
MATH 10701
Quiz #3 solutions
1. (10 points) Either calculate the result of each arithmetic operation, or explain why it cannot be performed. -3 1 (a) (4 points) 2 5 Squaring a matrix is taking a product, and it is possible in this case: -3 1 (-3)(-3) + 1