Believe it or not, algebra exists for a reason other than lowering a high school student's grade point average. Systems of linear equations, or a set of equations with two or more variables, are an essential part of finding solutions with only limited information, which happens to be exactly what algebra is. As a required part of any algebra student's life, it is best to understand how they work, not only so an acceptable grade is received, but also so one day the systems can be used to actually find desired information with ease.

There are three main methods of defining a system of linear equations. One way is called a consistent, independent solution. This essentially means that the system has one unique, definite solution. In this situation on a graph, a set of two equations and two variables would be solved as one single point where two lines intersect. It is much the same with three variables and three equations. The only difference is that the point is an intersection of three planes instead of two lines.

Additionally, there are situations where a system of linear equations could be described as consistent, dependent. These systems of linear equations have an infinite number of solutions where a general solution is used to substitute one or two variables for one other selected variable, and solves the other unknown variable or variables in terms of that selected one. Graphically when this system of linear equations is solved for two equations and two variables, the result is lines that coincide, or lay on top of each other, making any point on that line true for the system. A system with three equations and three variables would yield an answer that shows the three planes intersecting on a line or overlaying each other. When the system yields three planes intersecting on a line, all points on the line would make the systems true, and when planes coincide, all points on the coincidental planes would be correct when placed in the system for the variables....

...Solving systems of linearequations
7.1 Introduction
Let a system of linearequations of the following form:
a11 x1
a21 x1
a12 x2
a22 x2
ai1x1 ai 2 x2
am1 x1 am2 x2
a1n xn
a2 n x n
ain xn
amn xn
b1
b2
bi
bm
(7.1)
be considered, where x1 , x2 , ... , xn are the unknowns, elements aik (i = 1,...

...2012–13 First Semester MATH 1111 Linear Algebra Chapter 1: Matrices and Systems of Equations
Coverage of Chapter 1: Skip Application 3 in Section 1.4. Skip ‘Triangular Factorisation’ in Section 1.5.
A.
Solving Equations
1.
We are all familiar with solving equations. Illustrate how the following equations can be solved, and then raise and answer some theoretical and/or practical questions...

...the following matrices.
-4 8 (2 marks)
0 1
1 -3 -2 (3 marks)
2 -4 -3
-3 6 +8
Find the values of x and y if:(5 marks)
x + 2y 14 = 4 14
-3 y-2 -3 7+3x
Solve the following simultaneous equations using matrix method.
3x + y = 4
4x + 3y = 7(5 marks)
Find the value of K which makes a singular matrix.(3 marks)
3 1
4 -2
4 K 0
Calculate the cross product of the vector U = 2i – 3j – k and V = i + 4j –...

...The purpose of this project is to solve the game of Light’s Out! by using basic knowledge of Linear algebra including matrix addition, vector spaces, linear combinations, and row reducing to reduced echelon form. |
Lights Out! is an electronic game that was released by Tiger Toys in 1995. It is also now a flash game online. The game consists of a 5x5 grid of lights. When the game stats a set of lights are switched to on randomly or in a pattern. Pressing one...

...LINEAR ALGEBRA
Paul Dawkins
Linear Algebra
Table of Contents
Preface............................................................................................................................................. ii Outline............................................................................................................................................ iii Systems of Equations and...

...- FILS
Systems of Differential Equations and Models in Physics, Engineering and Economics
Coordinating professor: Valeriu Prepelita
Bucharest,
July, 2010
Table of Contents
1. Importance and uses of differential equations 4
1.1. Creating useful models using differential equations 4
1.2. Real-life uses of differential equations 5
2. Introduction to differential equations 6
2.1. First...

...Mathematical Economics.These Economists not only learnt Higher Mathematics with perfection but also applied it successfully in their higher pursuits of both Macroeconomics and Econometrics. A Mathematical formula (involving stochastic differential equations) was discovered in 1970 by Stanford University Professor of Finance Dr.Scholes and Economist Dr.Merton.This achievement led to their winning Nobel Prize for Economics in 1997.This formula takes four input variables-duration...

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