8/18/2019 CHE555 Procedure Lab 3

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Prepared by Madam Rabiatul Adawiyah Abdol Aziz (2016) Page 1

CHE555 NUMERICAL METHODS & OPTIMIZATION

LAB 3: LINEAR ALGEBRAIC EQUATION

Task 1: TO SOLVE MATRIC X IN MATLAB

Procedure:

(a) Define matrices A and B on the command window.(b) Then, use A\B command to find matric X.

Example:

2X 1 – X2 + 3X 3 = 5

-4X 1 – 3X 2 – 2X 3 = 8

3X 1 + X 2 – X3 =4

In Command Window:

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Prepared by Madam Rabiatul Adawiyah Abdol Aziz (2016) Page 2

Task 2: TO SOLVE MATRIC X BY USING CRAMER’S RULE IN MATLAB

Procedure:

(a) Define matric A, determinant of X1, X2 and X3 in the m-file.

(b) Then, use Cramer’s rule equation to find matric X.(c) After that, click save and run.

Example:

2X 1 – X2 + 3X 3 = 5

-4X 1 – 3X 2 – 2X 3 = 8

3X1 + X

2 – X

3 =4

In m-file:

Answer in command window:

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Prepared by Madam Rabiatul Adawiyah Abdol Aziz (2016) Page 4

Task 4: TO SOLVE MATRIC X IN EXCEL

Procedure:

(a) Define matrices A and B.

(b) To find inverse for matric A, select 3x3 box, type =minverse(select matric A). Then, clickF2 and simultaneously press (ctrl, shift and enter) button.

(c) To find matric X, select 3x1 box, type =mmult(select matric A inverse, select matric B).Then, click F2 and simultaneously press (ctrl, shift and enter) button.

Example:

2X 1 – X2 + 3X 3 = 5

-4X 1 – 3X 2 – 2X 3 = 8

3X 1 + X 2 – X3 =4

In Excel:

Task 5: EXERCISE

3X 1 – 0.1X 2 – 0.2X 3 = 7.85

0.1X 1 + 7X 2 – 0.3X 3 = -19.3

0.3X 1 – 0.2X 2 + 10X 3 = 71.4