The magic square is an arrangement of numbers in a square grid in such a way tha
ID: 2080653 • Letter: T
Question
The magic square is an arrangement of numbers in a square grid in such a way that the sum of the numbers in each row, and in each column, and in each diagonal is the same. MATLAB has a built-in function _magic(n) that returns an n times n magic square. In a script file create a (5 times 5) magic square, and then test the properties of the resulting matrix by finding the sum of the elements in each row, in each column and in both diagonals. In each case, use MATLAB's built-in function _sum. (Other functions that can be useful are diag and fliplr.)Explanation / Answer
Matlab code is as given below
-------------------------------------------------------------------------------------Start of code
% Program to create a magic square and verify it
clc
M= magic(5)
% To find sum of elements of each row
r1= sum(M(1,:)) % Sum of row 1
r2= sum(M(2,:)) % Sum of row 2
r3= sum(M(3,:)) % Sum of row 3
r4= sum(M(4,:)) % Sum of row 4
r5= sum(M(5,:)) % Sum of row 5
% To find sum of each coloumn
c1= sum(M(:,1)) % Sum of coloumn 1
c2= sum(M(:,2)) % Sum of coloumn 2
c2= sum(M(:,3)) % Sum of coloumn 3
c2= sum(M(:,4)) % Sum of coloumn 4
c2= sum(M(:,5)) % Sum of coloumn 5
% To find sum of diagonal
d1= sum(diag(M)) % Sum of principal diagonal elements
d2= sum(diag(fliplr(M)))
-------------------------------------------------------------------------------End of code
Following results are obtained when executed.
M =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
r1 =
65
r2 =
65
r3 =
65
r4 =
65
r5 =
65
c1 =
65
c2 =
65
c2 =
65
c2 =
65
c2 =
65
d1 =
65
d2 =
65
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