When given a standard linear model: $Y= X_1B_1 + X_2B_2 + e$ where $Y: n \times 1$ and $Xi: n \times p$
I am having difficulty showing that $B_1$ is only estimable when $rank(Q_2X_1)= p_1$
where $Q_2 =$ the orthogonal projection onto the orthogonal complement of the column space of $X_2$
I know the general idea behind estimability for regression parameters, but am just having a bit of trouble comprehending this question. Thank you for any help!