## OLS estimate of Beta in General Linear Model

Hi,

I have an assignment with part of the question asking me to determine the OLS estimate of Beta given the conditions that

$y = X\beta + u, u$ ~ $N(0, \sigma^2I)$

where $X$ is $n x p$ non-stochastic and of rank $p$

I have to take the case $p = 2$ and the matrix X has the form where there are $r$ 1's in the first column with the rest 0's and $s$ 1's in the second column with the rest 0's and with $n = r + s$ (i.e. each row has a 1 and 0 in it, with the 1 in the first column for the first r rows and in the second column for the last s rows).

This leaves the column vector $\beta = (\beta_1, \beta_2)$. As I said I must determine the OLS estimate of $\beta$ in this case. Help?