This document presents an example of using Gauss's elimination method to solve a system of linear equations. The example involves determining the amounts of three antigens (A, B, C) needed from three sources (x, y, z) to meet the needs of a lab technician. The system is set up as a matrix and Gauss's elimination method is applied to row reduce the augmented matrix and solve for x, y, z using back substitution. The solution found is x=6.5, y=1, z=7.5, representing the amounts required from each source.
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SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
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Cosmetic shop management system project report.pdf
GUASS’S ELIMINATION METHOD AND EXAMPLE
1.
2. GROUP NAME: BANGUL KHAN(F16BM05)
DEPARTMENT: BIOMEDICAL ENGINEERING(MUET)
PRESENTATION SUBJECT : LAAG.
PRESENTATION TOPIC : GUASS’S ELIMINATION METHOD AND
EXAMPLE.
3. GUASS’S ELIMINATION METHOD:
It is method which is used to solve
the non homogenous system of linear equation with square.
This method has four steps:
Convert the system of linear equation into matrix form.
Ax=b
Construct the Augmented matrix which is denoted by Ab or A/B
4. Use eliminatory row operation on Augmented matrix to find
echelon form.
1 X X
0 1 X
0 0 1
ECHELON
MATRIX
6. Example :
A lab technician needs 15% amount of Antigen-A, 30% of Antigen-B
and 45% of Antigen-C to test the blood Group. There is three sources
( x y z ) where these antigen can be obtained and composition of Antigen-A ,
Antigen-B and Antigen-C according to sources are given below.
ANTIGEN SOURCE x SOURCE y SOURCE z
A 1 1 1
B 1 2 3
C 1 2 5
7. Using Guass elimination method to determine the required amount of
Antigen-A , Antigen-B and Antigen-C that must be satisfied from the tabular
sources in order to meet the lab technician need?
SOLUTION:
Let x, y, z be the sources of each antigen so according to question
first we made linear equation of each antigen then we apply Guass’s elimination
method .
9. So , Apply steps of Guass elimination method to find the answer.
Step no 1:
Convert the system of linear equation into matrix form.
Ax = b
1 1 1 X 15
1 2 3 y = 30
1 2 5 z 45
10. Step no 2:
Construct the Augmented matrix which is denoted by Ab or A/B
1 1 1 . 15
Ab = 1 2 4 . 60
1 2 5 . 45
Augmented
matrix
14. Step no 4:
Using backward substitution on echelon matrix to find the answer of
problem.
1 1 1 . 15
Ab = 0 1 2 . 15
0 0 2 . 15
x + y+ z = 15
y + 2z = 15
2z = 15
