Aloha :)
Die Covarianz ist eine Bilinearform, d.h. linear in beiden Argumenten:
$$\phantom{=}\operatorname{Cov}(5X_1-X_2, X_1-19X_2)$$$$=\operatorname{Cov}(5X_1, X_1-19X_2)+\operatorname{Cov}(-X_2, X_1-19X_2)$$$$=5\operatorname{Cov}(X_1, X_1-19X_2)-\operatorname{Cov}(X_2, X_1-19X_2)$$$$=5\left(\operatorname{Cov}(X_1, X_1)+\operatorname{Cov}(X_1,-19X_2)\right)-\left(\operatorname{Cov}(X_2, X_1)+\operatorname{Cov}(X_2,-19X_2)\right)$$$$=5\left(\operatorname{Cov}(X_1, X_1)-19\operatorname{Cov}(X_1,X_2)\right)-\left(\operatorname{Cov}(X_2, X_1)-19\operatorname{Cov}(X_2,X_2)\right)$$$$=5\left(\sigma_1^2-19\sigma_{12}\right)-\left(\sigma_{12}-19\sigma_2^2\right)$$$$=5\sigma_1^2-95\sigma_{12}-\sigma_{12}+19\sigma_2^2$$$$=5\sigma_1^2-96\sigma_{12}+19\sigma_2^2$$$$=5\cdot2-96\cdot3+19\cdot15=7$$