How to create Matrix [1 2 3 4; 2 4 6 8; 3 6 9 12; 4 8 12 16] without using loops or any functions using loops?

Hi, I'm trying to generate matrix

A = [1 2 3 4; 2 4 6 8; 3 6 9 12; 4 8 12 16]

without using any loops, but I have trouble finding solution

Answer 1

[James Tursa]

n = 4; % whatever
result = (1:n) .* (1:n)' % use implicit expansion row .* column

result = 4×4

1 2 3 4 2 4 6 8 3 6 9 12 4 8 12 16

Answer 2

[David Hill]

A = [1 2 3 4; 2 4 6 8; 3 6 9 12; 4 8 12 16];%what is wrong with this

You could also do something like:

n=4;
A=[1:n;2:2:2*n;3:3:3*n;4:4:4*n];

[Milosz Sobczyk]

Nothing is wrong. It was just an example I've written so I can expand a solution to NxN matrix. Thanks for help

Answer 3

[Davide Masiello]

To make it more general

n = 4;
a = 1:n;
A = repmat(1:n,n,1).*a';

For instance, if n = 6 this will generate

A =

     1     2     3     4     5     6
     2     4     6     8    10    12
     3     6     9    12    15    18
     4     8    12    16    20    24
     5    10    15    20    25    30
     6    12    18    24    30    36

not sure if repmat uses loops though, it probably does.

[Milosz Sobczyk]

Thanks. Even if it does it's still worth checking out.

[Davide Masiello]

No problem. Honestly, I kept thinking about it but I believe that a loop is necessary.

Without invoking predefined function, it could look like this.

n = 4;
A = zeros(n);

for i = 1:n
    A(i,:) = (1:n)*i;
end

Just in case, I'll follow this question. Will you please update it if you find a loop-less solution?

[Milosz Sobczyk]

Sure, I will. I'm asking since I had an exercise in school that required us to do this without loops.

[Milosz Sobczyk]

I've found it and it goes like this:

n = 8;
A = ones(n, 1) * (1:n)
A = A .* A'

[Davide Masiello]

That's great, thanks!