HOMEWORK 1

Q1. Write a MATLAB® program to calculate the solution x for Ax=y using Gauss elimination method (with pivoting and normalization), where A is a coefficient matrix of any size.

Hints:

Use m-files to create a general function

Make use of loops and if statements as necessary

Remember

,

i.e. M=[a_i,j] where i=1:3 and j=1:3.

When you define a 3-by-3 matrix in the command window, say M1, you should call the function you wrote in the m-file and the function will calculate the determinant.

Let me give you an example: The following is an m-file for a function named MySum.m that sums the elements of the matrix M

function [totalM]=SumFun(M)    %the function returns totalM,

totalM=M(1,1)+M(1,2)+M(1,3)+M(2,1)+ M(2,2)+M(2,3)+M(3,1)+ M(3,2)+M(3,3)  %Add the elements of the matrix

end

This code could alternatively be written as the following where M could be a matrix of any size:

function [totalM]=SumFun(M)    % the function returns totalM,

[m,n]=size(M);                       % assigns the size of M matrix to m and n

i=1;                                      %start at i=1

j=1;                                      %start at j=1

totalM=0;                              %start at totalM=0

for i=1:m                               % nested loop: increment i by 1 until m

for j=1:n,

    totalM=totalM+M(i,j);

end

end

totalM

To run this function, go to the command window and write a matrix

For example:

>> A=[ 1 2 3 4; 12 2 4 2; 34 3 1 6; 0 2 5 3]

>> SumFun(A)   %will give you the following answer

totalM =

    84

Q2. Solve the following set of equations in MATLAB® using

1. Matrix inversion

2. Gauss-Jordan relation

3. Cramer’s rule                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     

   x₁ +    x₂ + 3 x₃ = 1

   x₁ + 2 x₂ + 5 x₃ = 2

3 x₁ +    x₂ +    x₃ = 1