I am having trouble with the following problem regarding conditional expectation. Consider the random variables $X,Y$ and $Z$ with mean and dispersion matrix
$$\mu=\begin{bmatrix}1 \\ 1\\ 1\end{bmatrix},\ \Sigma=\begin{bmatrix}1 & \rho & \rho \\ \rho & 1 & \rho\\ \rho & \rho & 1\end{bmatrix}$$
Furthermore, consider the random variables $U=X+Y+Z$ and $V=2X-Y-Z$.
I am now asked to calculate $\text{E}\left(\begin{bmatrix}X\\ Y\end{bmatrix}\large{|}Z=z\right)$ and from my lecture notes I am told that computing this is done in the following way:
$$\text{E}(X_1|X_2=x_2)\mu_1+\Sigma_{12}\Sigma_{22}^{-1}(x_2-\mu_2)$$
where the normally distributed random variable $X$ has been partitioned into the following:
$$X=\begin{bmatrix}X_1\\X_2\end{bmatrix},\ \mu=\begin{bmatrix}\mu_1\\\mu_2\end{bmatrix},\ \Sigma=\begin{bmatrix}\Sigma_{11} & \Sigma_{12}\\ \Sigma_{21} & \Sigma_{22}\end{bmatrix}$$
I am completely confused with how I am supposed to use this with the formula given above. Can someone help me figure out how to determine what $\Sigma_{12}$ and $\Sigma_{22}$ is? I can't connect this to the given setting introduced in the problem.
Thanks in advance.