$X$ and $Y$ are jointly normal, with the mean vector and covariance matrix given by: $\mu= \begin{pmatrix} 1 \\ 2 \\ \end{pmatrix} \Sigma= \begin{pmatrix} 2 & 0.4 \\ 0.4 & 1 \\ \end{pmatrix}$ Let $Z_1=X+Y$ and $Z_2=2X-Y$. What is the mean vector and covariance matrix of $Z_1$ and $Z_2$?
What I did so far: I have calculated the mean and variance of $Z_1$ to be 3 and 3.8 respectively. The mean and variance of $Z_2$ are 0 and 7.4 respectively. So all I'm missing is the value for the covariance of $Z_1$ and $Z_2$ which is $\rho\sigma_{Z_1}\sigma_{Z_2}=\rho\sqrt{3.8}\sqrt{7.4}=5.303\rho$. How do I find $\rho$?