Illustration of gauss elimination, MATLAB in Engineering

Illustration of Gauss elimination:

For illustration, for a 2 × 2 system, an augmented matrix be:

384_Illustration of Gauss elimination.png

Then, the EROs is applied to obtain the augmented matrix into an upper triangular form:

2023_Illustration of Gauss elimination1.png

Therefore, the goal is simply to substitute a21 with 0. Here, the primes points that the values (might) have been changed.

Putting this back into the equation form results,

2339_Illustration of Gauss elimination2.png

Executing this matrix multiplication for each row outcomes in:

1133_Illustration of Gauss elimination3.png

 

Therefore, the solution is as shown below:

2336_Illustration of Gauss elimination4.png

Likewise, for a 3 × 3 system, the augmented matrix is decreased to upper triangular form:

1096_Illustration of Gauss elimination5.png

(This will be completed systematically by first obtaining a 0 in the a21 position, then a31, and lastly a32.)

Then, the answer will be:

1316_Illustration of Gauss elimination6.png

As an illustration, consider the 2 × 2 system of equations as shown below:

1276_Illustration of Gauss elimination7.png

As a matrix equation Ax = b, this is:

835_Illustration of Gauss elimination8.png

The initial step is to augment the coefficient matrix A with the b to obtain an augmented matrix [A| b]:

743_Illustration of Gauss elimination9.png

Posted Date: 10/22/2012 4:26:11 AM | Location : United States







Related Discussions:- Illustration of gauss elimination, Assignment Help, Ask Question on Illustration of gauss elimination, Get Answer, Expert's Help, Illustration of gauss elimination Discussions

Write discussion on Illustration of gauss elimination
Your posts are moderated
Related Questions
str2num function - String: The function str2num does the opposite; it takes the string in which a number is stored and converts it to the type double: >> num = str2num('123.

function numden: The function numden will return individually the numerator & denominator of a symbolic expression: >> sym(1/3 + 1/2) ans = 5/6 >> [n, d] =

Basic mathematical operations: All the basic mathematical operations can be executed on symbolic expressions and variables (example, add, raise to a power, multiply, subtract,

Function cellplot - Cell array: The function cellplot place a graphical display of the cell array in a figure Window; though, it is a high-level view and fundamentally just di

ischar function: The ischar function return the logical true if an array is a character array, or logical false if not. >> vec = 'EK127'; >> ischar(vec) ans =

Replacing, Finding, and separating strings: There are numerous functions which find and replace the strings, or parts of strings, within the other strings and functions which

. Generate the following signal, x(n)=1+cos((25*pi*n)/100),0 Compute the DTFT of x[n] for w=0:0.01:2*pi Plot the Real part, imaginary part, the amplitude and phas

Illustration of Passing arguments to functions: Here is an illustration of calling this function: >> printrand() The random # is 0.94 As nothing is passed to

Function issorted - set operations: The function issorted will return 1 for logical true when the argument is sorted in ascending order (minimum to maximum), or 0 for false wh

Vectors of Structures: In numerous applications, involving database applications, information generally would be stored in the vector of structures, instead of in individual s