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1)write and test code to generate the squate matrix A for a user specified N whe

ID: 2993554 • Letter: 1

Question


1)write and test code to generate the squate matrix A for a user specified N where


     1 2 3 ..............N

     2 3 4 ..............N+1

A=3 4 5 ..............N+2

      ...

      ....

    N N+1 N+2 ......2N-1


That is A(i,J)= i+j-1.

Hint if A=ones(3,3) and D=diag{[1 2 3] then c=D*A will produce Mat Lab output


2) generatethe matrix B(i,j)= 1/(i,j-1) then for a 3x3, B= 1 1/2 1/3

1/2 1/3 1/4

1/3 1/4 1/5


use dot notation



3) Tabulate the determinant of B for N=1,2 .....5.

Hint use mat lab help to find dederminant function


Explanation / Answer

##a)

N = input('Enter a number : ');

D=ones(N,N);

A=zeros(N,N);

for i=1:N

A(i,i)=i;

end


C=D*A;


for i=1:N

for j=1:N

C(i,j)=C(i,j)+i-1;

end

end

C


OUTPUT--

Enter a number : 3


C =


1 2 3

2 3 4

3 4 5



b)


N = input('Enter a number : ')


D=ones(N,N);


A=zeros(N,N);


for i=1:N


A(i,i)=i;


end



C=D*A;



for i=1:N


for j=1:N


C(i,j)=C(i,j)+i-1;


end


end




B=ones(N,N)./(C);




format rat


B


OUTPUT--

Enter a number : 3


B =


1 1/2 1/3

1/2 1/3 1/4

1/3 1/4 1/5



c)for N=1:5

D=ones(N,N);

A=zeros(N,N);

for i=1:N

A(i,i)=i;

end


C=D*A;


for i=1:N

for j=1:N

C(i,j)=C(i,j)+i-1;

end

end

B= ones(N,N);

for i=1:N

for j=1:N

B(i,j)=1/(C(i,j));

end

end

Z(N)=det(B);

end

fprintf('number determinant ')

for i=1:5

fprintf('%d %.20f ',i,Z(i))

end


Output---

number determinant

1 1.00000000000000000000

2 0.08333333333333331500

3 0.00046296296296296135

4 0.00000016534391534393

5 0.00000000000374929513