Hints for problem 3.3(a)

Let \(\tilde{\theta}= \boldsymbol{c}^T \boldsymbol{y}\) be any other linear unbiased estimator of $a^T \beta$ and let $c^T = a^T (X^T X)^{-1} X^T + d^T$. Compute $E[\tilde{\theta}]$ and conclude based on the result that $d^T X = 0$. Compute $Var(\tilde{\theta})$ and express it as $Var(\hat{\theta}_{LS})$ plus a positive constant.