Linear models — variances of uncorrelated least squares estimators

Consider the linear model

$$Y_1=\beta_1+\beta_2+\epsilon_1,\qquad Y_2=\beta_1+2\beta_2+\epsilon_2,\qquad Y_3=\beta_1+c\beta_2+\epsilon_3,$$

where $\beta_1,\beta_2\in\mathbb{R}$ are unknown parameters, and the uncorrelated errors $\epsilon_i$, $i=1,2,3$ have zero mean and finite variance $\sigma^2(>0)$. The constant $c$ is such that $\hat\beta_1$ and $\hat\beta_2$ are uncorrelated, where $\hat\beta_1$ and $\hat\beta_2$ are the best linear unbiased estimators of $\beta_1$ and $\beta_2$, respectively. Which of the following statements is the correct option for $(\operatorname{Var}(\hat\beta_1),\operatorname{Var}(\hat\beta_2))$?