Let $y_i=\Sigma^k_{j=0} x_{ij} \beta_j+\epsilon_i$
$\epsilon_i$ is $NID(0,\sigma^2)$ and $x_{ij}, i=1,...,n, j=0,...,k$ is the $(i,j)^{th}$ elelement of the $n \times (k+1)$ matrix $X$, which is of full rank, and $\beta_o,...,\beta_k$ are constants. Also $g_{ij}$ is the $(i,j)^{th}$ element of the matrix $(X'X)$. The first column of $X$ corresponds to $j=0$
Specifying the value of $M_{kj}$, show that the least squares estimate of $\beta_{k-1}$ is given by $\Sigma^n_{i=1}y_i\Sigma^k_{j=o}x_{ij}M_{kj}$
I have no idea how to approach this one. Please can someone give me some pointers? I am familiar with getting estimates of $\beta$ where there are only two (ie $\beta_0, \beta_1$) but not when there are lots. Presumably matrix algebra is involved? I really don't know where to start.