# creating a script to solve simultaneous equations using matrices

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Callum Davies on 23 Dec 2022
Edited: Vijay on 26 Dec 2022
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 on 23 Dec 2022
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 on 23 Dec 2022
- 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?

Vijay on 26 Dec 2022
Edited: Vijay on 26 Dec 2022
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