Matrix Solution

The elements of the symmetric Pascal matrix are obtained from: Pij = (i + j - 2)!/(j - 1)!(j - 1)! Write a MATLAB program that creates an n by n symmetric Pascal matrix. Use the program to create a 4x4 and 7x7 Pascal matrices.

[Joshua Magno]

function X=matrix

n=input('Enter the number of rows: ');

m=input('Enter the number of columns: ');

A=[]; % define an empty matrix

for k=1:n

for h=1:m if k==1

A(k,h)=k;

elseif h==1

A(k,h)=h;

else

A(k,h)=A(k,h-1) + A(k-1,h); %assign values to other elements

end

end

end

    A

Answer 1

[Amith Kamath]

for i = 1:7
for j = 1:7
P(i,j) = factorial(i + j - 2)./(2*factorial(j - 1));
end
end

for a 4x4 matrix, change the 7 in lines 1 and 2 to 4! But with this formulation, I wonder how it can be symmetric. I'm guessing you've mistyped the question and the denominator has to be (i-1)!(j-1)! which will set things correct!

http://en.wikipedia.org/wiki/Pascal_matrix

and hence the line 3 in the code above will be:

P(i,j) = factorial(i + j - 2)./(factorial(j - 1)*factorial(i - 1));

Oh, and BTW, MATLAB (as usual), has a function called pascal, and you need to just say pascal(4) or pascal(7)!

Answer 2

[Andrei Bobrov]

n = 7;
k = factorial(0:n-1);
out = factorial(bsxfun(@plus,1:n,(1:n)')-2)./bsxfun(@times,k,k');