Needs a MATLAB code. Exercise 2.6 solution A = rand(3) 0.814 0.913 0.278 0.905 0

Question

Needs a MATLAB code.

Exercise 2.6 solution

A = rand(3)

0.814   0.913    0.278

0.905   0.632    0.546

0.127   0.097    0.957

A(1: size(A,1) + 1:end)

ans = 0.814   0.632   0.957

Prints out the diagnol elements of the matrix A.

Suppose x is a column vector. Compute, without using loops or conditionals, the matrix A given by a_ij = {1/(x_i - x_j)^2 if i plusminus j, 1 otherwise. (One way to do this uses direct assignment to the diagonal elements of A. Using row/column style indices, this is rather tricky, but sec Exercise 2.6.) Suppose A is any matrix. What does this statement do? A(1: size(A, 1) + 1: end)

Explanation / Answer

x=rand(3,1); % For geting column vector x
A=zeros(3,3); % For initilization of A by zero
A(1: size(A,1) + 1:end)=1; % Assigining digonal vector

A(1,2)=1/((x(1,1)-x(2,1)).^2); % For first row
A(1,3)=1/((x(1,1)-x(3,1)).^2);

A(2,1)=1/((x(2,1)-x(1,1)).^2); % For second row
A(2,3)=1/((x(2,1)-x(3,1)).^2);

A(3,1)=1/((x(3,1)-x(1,1)).^2); % For third row
A(3,2)=1/((x(3,1)-x(2,1)).^2);

You can also solve the problem using index as matrix

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