MATH 204
Concordia University ( )
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MATH 204: Vectors and Matrices Questions & Answers
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MATH 204: Vectors and Matrices Questions & Answers 

Problem 1
Using the Gauss-Jordan method (i.e. reduced row echelon form method), find all the solutions of the following system of equations:

2x − 2y	 2u 3v		= 1 3x − 3y − z 5u 2v	= 3 2x − 2y − 2z 6u		= −2.

Solution 1
Writing the system as an augmented matrix and performing elementary row operations,
 
2 −2	0	2 3	1 	1 −1	0	1	3/2
 
1/2
 
3 −3 −1 5 2	3 → 0	0	−1 2 −5/2
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MATH 204 Summary Complete
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MATH 204 Summary 
Linear equation in the n variables x1, x2, … , xn to be on that can be expressed in the form: 
a1x1 a2x2 … anxn=b
In special case where b = 0, it is called a homogeneous linear equation in the variables x1, x2, … , xn.
A finite set of linear equations is called a system of linear equations or a linear system.
The variables are called unknowns.
A solution of a linear system in n unknowns can be written as (s1, s2, … , sn) which is called an ordered n-tuple. If n = 2,...
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