If I have the model:
$y = β_1x_1 + β_2x_2 + u$.
I have to show that the OLS estimator is:
I think that I have to use $\beta =\begin{pmatrix} \beta_1 \\ \beta_2 \end{pmatrix}=(X^tX)^{-1}X^tY$. But I'm a but confused. Can someone write up the matrices X and Y? I only have to multiply the first coordinat in the $2\times1$, because I only have to show it for $\beta_1$?
$$\require{cancel} \xcancel{ X = \left[ \begin{array}{ccc} 1 & x_{11} & x_{12} \\ \vdots & \vdots & \vdots \\ 1 & x_{n1} & x_{n2} \end{array} \right]. \qquad\qquad Y = \left[ \begin{array}{c} y_1 \\ \vdots \\ y_n \end{array} \right]. \qquad {}} $$
Later edit: I failed to notice that the model proposed in the original posting does not have an intercept. So that means we have $$ X = \left[ \begin{array}{cccc} x_{11} & x_{12} \\ \vdots & \vdots \\ x_{n1} & x_{n2} \end{array} \right]. \qquad\qquad Y = \left[ \begin{array}{c} y_1 \\ \vdots \\ y_n \end{array} \right]. $$