From equation to matrix with for loop

How can somone change equation into matrix with a for loop? For example if you have something like this:

for i = 1:10
    1*x(i) + 2*x(i+1) + 3*x(i+2) = y(i)
end

So, if I were to do this by hand it would be like for i =1

[ 1 2 3 ] * [ x(1) x(2) x(3)]' = y(1)

and for i = 2 you will have

[ 1 2 3 ] * [x(2) x(3) x(4)]' = y(2)

so how can I structure this in a way it gives me a matrix that looks like this:

[ 1 2 3 0; 0 1 2 3] * [x(1) x(2) x(3) x(4)]' = [y(1); y(2)]

[Bopha NEAK]

for i = 1:10

1*x(i) + 2*x(i+1) + 3*x(i+2) = y(i)

end

[Image Analyst]

@Bopha NEAK, You can't have the y be on the right side of the equal sign. It must be on the left. See my answer below.

Answer 1

[Image Analyst]

Do you mean like this:

x = 1 : 12
numRows = 3; % Whatever you want.
y = zeros(numRows, length(x)); % Preallocate.
for row = 1 : numRows
	for col = row : length(x) - 2 % Can't have col+2 be longer than x
		y(row, col) = 1*x(col) + 2*x(col+1) + 3*x(col+2);
	end
end
y

x =

1 2 3 4 5 6 7 8 9 10 11 12

y =

14 20 26 32 38 44 50 56 62 68 0 0

0 20 26 32 38 44 50 56 62 68 0 0

0 0 26 32 38 44 50 56 62 68 0 0

[Io7]

Thank you for your reply, that really helped, but I wanted to know if there is a way to make Matlab do it instead of specifiying the number of rows because for example if I have like a large matrix, It will be hard to try to specify the number of X's so I won't be able to tell the number of rows

also for this 1*x(i) + 2*x(i+1) + 3*x(i+2) = y(i) I'm just trying to make it simple as possible but it can be more complicated like 1*x(i) + 2*x(i+1) + 3*x(i+2) = y(i)+y(i-1)/2

but what I'm trying to know if there is a way matlab can arrange the matrix for me and structure it the way I want

so for the example I gave

So, if I were to do this by hand it would be like for i =1

[ 1 2 3 ] * [ x(1) x(2) x(3)]' = y(1)

and for i = 2 you will have

[ 1 2 3 ] * [x(2) x(3) x(4)]' = y(2)

and for i = 3 you will have

[ 1 2 3 ] * [x(3) x(4) x(5)]' = y(3)

so I want matlab to structure my matrix in this form

[ 1 2 3 0 0; 0 1 2 3; 0 0 1 2 3] and this will be a single matrix <-- I want matlab to generate this matrix for me

[x(1) x(2) x(3) x(4) x(5)]' and this is another matrix

then it will equal to

[ y(1); y(2); y(3)] the result matrix

[Image Analyst]

I really don't know what

1*x(i) + 2*x(i+1) + 3*x(i+2) = y(i)+y(i-1)/2 

means. You can't have an assignment like that in MATLAB. Are you trying to do differential equations?