Initialise
Clear the workspace and load Linear Algebra package
> restart;
> with(LinearAlgebra):
If you want practice at hand calculation you should use the worksheet "Interactive Gaussian Elimination" (see Menu) Enter the matrix of coefficients and right-hand side vector You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View, Palettes) > A:=; > b:=;

Form the augmented matrix and solve
The Maple routine GaussianElimination requires the augmented matrix A|b as input. In this worksheet this matrix is called Ab and is formed using > Ab:=;
The row echelon form H|c (here called Hc) of Ab is computed by GaussianElimination. (For a square system of equations the row echelon form of A is upper triangular ) Note that the Maple function GaussianElimination performs a systematic version of the idea of elementary row operations: (i) Multiples of R1 are subtracted from R2, R3 . . Rn to reduce the elements below the leading diagonal in the first column to zero. (ii) In the resulting system multiples of R2 are subtracted from R3, R4 . . Rn to reduce the elements below the leading diagonal in the second column to zero. (iii) This process is continued to produce a system in row echelon form, using essential row interchanges where necessary. > Hc:=GaussianElimination(Ab);

Look at the form of H|c before executing the next statement. Is there a unique solution, infinitely many solutions or no solution ? The solution vector, x, is found from H|c using BackwardSubstitute x:=BackwardSubstitute(Hc);

Maple techniques: Accessing vector components and matrix elements and checking that Ax = b The components of x are x[1], x[2] ....:
> x[1];
> x[2];

The elements of A are A[i,j], for example:
A[2,1];

...Summer 2010-3 CLASS NOTES CHAPTER 1
Section 1.1: LinearEquations
Learning Objectives:
1. Solve a linearequation
2. Solve equations that lead to linearequations
3. Solve applied problems involving linearequations
Examples:
1. [pic]
[pic]
3. A total of $51,000 is to be invested, some in bonds and some in...

...Patterns within systems of LinearEquations
HL Type 1 Maths Coursework
Maryam Allana
12 Brook
The aim of my report is to discover and examine the patterns found within the constants of the linearequations supplied. After acquiring the patterns I will solve the equations and graph the solutions to establish my analysis. Said analysis will further be reiterated through the creation of numerous...

...2014/9/16
LinearEquations
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LinearEquations
A linearequation is an equation for a straight line
These are all linearequations:
y = 2x+1
5x = 6+3y
y/2 = 3 x
Let us look more closely at one example:
Example: y = 2x+1 is a linearequation:
The graph of y = 2x+1 is a straight line
...

...Algebra I Chapter 5 Study Guide Writing LinearEquations
Name ________________
Due: Tuesday, January 17 (Exam week)
100 points
Writing LinearEquations in a Variety of Forms
Using given information about a __________, you can write an ________________of the line in _____________ different forms. Complete the chart:
Form (Name)
Equation
• •
Important information
The slope of the line is ____. The __ -...

...SYSTEM OF LINEAREQUATIONS IN TWO VARIABLES Solve the following systems: 1.
x y 8 x y 2
by graphing
by substitution
by elimination
by Cramer’s rule
2.
2 x 5 y 9 0 x 3y 1 0
by graphing
by substitution
by elimination
by Cramer’s rule
3.
4 x 5 y 7 0 2 x 3 y 11 0
by graphing
by substitution
by...

...direction of the jetstream. The return trip against the jetstream took four hours. What was the jet's speed in still air and the jetstream's speed?
3 ) These circles are identical. What is the value of x ?
4 ) Solve for x using these two equations: 2x + 6 = y; y - x = 2
5 ) The perimeter and the area of this shape are equal. What is the value of x?
6) Shobo’s mother’s present age is six times Shobo’s present age . Shobo’s age five years from now will be one...

...CHAPTER 8
Linear Programming Applications
Teaching Suggestions
Teaching Suggestion 8.1: Importance of Formulating Large LP Problems.
Since computers are used to solve virtually all business LP problems, the most important thing a student can do is to get experience in formulating a wide variety of problems. This chapter provides such a variety.
Teaching Suggestion 8.2: Note on Production Scheduling Problems.
The Greenberg Motor example in this chapter...

...Forum #2: LinearEquations in Real Life
Pick one of the following problems. Show how you would solve it using a system
of linearequations.
1) John spent $201 shirts and pants for work. Shirts cost $27 and pants cost $22. If he
bought a total of 8 articles of clothing, then how many of each kind did he buy?
2) A school dance has 228 students. There are 63 fewer girls than twice as many boys.
How many boys and girls attended the dance?...

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