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







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