Error saying matrices are not the same size

I am trying to perform Euler's method for a system of ODE's but when I run the function I keep getting this error "Unable to perform assignment because the size of the left side is 11-by-1 and the size of the right side is 11-by-2", or something like it depending on where I put the colons on the first w in the for loop. I

f=@(t,w) [t*w(2),w(1)*w(2)-t*w(1)];

function [t,w] = eulerSys(f,range,iv,h);
% input f is a vector valued function containing the system of differential equations
%       f takes t and w as inputs, where w is an array containing the dependent variables
%       the output f should be organized as a row vector
% input range is a vector of length 2 containing an initial time and a final time
% input iv is a vector containing the initial conditions for each dep variable
% input h is a scalar step size
% output t is a column vector containing the times at which we have solution approximations
% output w is a matrix whose columns are the approximations of the different dep variables

%set up an evenly spaced array for t
t = (range(1):h:range(2))';

% Preallocate the solution matrix w.  Use the length of t to determine the number of time steps 
% and the length of iv to determine the number of functions/ODEs.
% Make sure the matrix is tall, not wide.  That is, each column of w should represent one function.
w=zeros(2,length(t))';
w(1,1)=iv(1);
w(1,2)=iv(2);

%input the initial conditions into the first row of w

w
%run through Euler's method to fill in the remaining rows of w
for i = 2:length(t)-1;
    w(:,2) = w(:,i)+h*f(t,w(:,i))
end

This is the code that I have for the function, and when I run the function it creates a [11x2] matrix for w, but then for some reason when it runs the for loop it just completely messes it up and changes it to a [11x1] matrix. If I change where the colons are in the foor loop it will either give me a similar error or it just won't work at all.

Answer 1

[KSSV]

I think the loop should be something like this:

for i = 2:length(t)-1;
    w(i,:) = w(i-1,:)+h*f(t(i),w(i-1,:)) ; 
end

In your code, now your input is complete t. which is a vector and the output will be a vector which you don't want. You need to send the time value at that loop. Also you messed up the indexing in w.