Basics-

How to create a matrix M1 in which each entry is the sum of the row index number and the column index number???

second question

How to create a matrix X that is equal to the matrix product of a and c ( which are previously created) =[1 1 1;0 1 1;0 0 1]

Answer 1

[Matt Fig]

% Create an m-by-n matrix where each element is sum of row and col position.
D = ones(m,n);
[I,J] = find(D);
D(:) = I+J

Another way too:

D = ones(m,n);
D(:) = ceil((1:m*n)/m) + rem((1:m*n)-1,m) + 1

Your second question is not clear. Elaborate.

Answer 2

[Walter Roberson]

I am not sure what the matrices "a" and "c" represent, but matrix multiplication between the two would be X = a*c .

For the matrix M1:

m = 5; n = 6; mn = max(m,n);
t = hankel(2:mn+1) + fliplr(flipud(hankel([2*mn:-1:mn+2 0])));
M1 = t(1:m,1:n);

... Not that Matt's answer won't work fine, but sometimes it is nice to know about alternatives.

But the cleaner version of what Matt proposed is:

M1 = bsxfun(@plus,(1:m).',1:n);