creating a script to solve simultaneous equations using matrices

i need help to Write a script file to solve a system of simultaneous equations that is written in the form 𝐴𝑋 = 𝐵 where 𝐴 is a square matrix of dimensions 𝑛 × 𝑛 The script file must • Ask for the definition of matrices 𝐴 and 𝐵 • Check that matrix 𝐴 is square and display an appropriate message if it is not square. • Check whether a solution exists and display an appropriate message if a solution does not exist. • Calculate the solution for 𝑋 if it exists and display the value of 𝑋 with some appropriate text.

I have started but wasnt able to get very far as i am completely stuck and dont know where to go from here. Any help would be greatly appreciated. Here is how far i have gotten with the code.

% Reset the script

clc

clear all

close all

% Get input of the variables of the simultanious equations

a=input("First equation co-efficient of x: ");

b=input("First equation co-efficient of y: ");

c=input("Second equation co-efficient of x: ");

d=input("Second equation co-efficient of y: ");

e=input("First equation content term: ");

f=input("Second equation content term: ");

%set up the matrices

A=[a,b;c,d];

X=[x;y];

B=[e;f];

[Callum Davies]

i know how to do the maths between the matrices but im not sure how to define x and y as their values are unknown. Im also unsure what format to present the output

[Dyuman Joshi]

- How would you check if a matrix is square?

For the equation A*X=B, the solution is X = (A inverse) * B.

- So, to check if a solution exists or not, what is the condition?

Answer 1

[Vijay]

Hello @Callum Davies

You can use the program below to solve the equations.

% code section 
% Reset the script 
clc 
clear all 
close all 
% Get input of the variables of the simultanious equations 
a=input("First equation co-efficient of x: "); 
b=input("First equation co-efficient of y: "); 
c=input("Second equation co-efficient of x: "); 
d=input("Second equation co-efficient of y: "); 
e=input("First equation content term: "); 
f=input("Second equation content term: "); 
%set up the matrices 
A=[a,b;c,d]; 
%X=[x;y]; 
B=[e;f]; 
X = A\B; 
%X will be a matrix of 2 x 1; 

In case the solution does not exist you will have "Inf" values in matrix X. you can check that using isfinite method and provide a response a suitable response.

Hope that helps