Generating correlated standard normals

Question

Suppose I want to generate three standard normals $X, Y, Z$ with correlation matrix given by

$R$= $ \begin{pmatrix} 1.0 & 0.2 & 0.2 \\ 0.2 & 1.0 & 0.2 \\ 0.2 & 0.2 & 1.0\end{pmatrix}$

How would I do this?

Edit: I would give a starting point for discussion, but I don't understand what it means to "generate" a variable to begin with. I am trying to further my understanding before finals.

Answer 1

Transform to a basis in which the matrix is diagonal (its eigenvalues are $1.4$ and $0.8$ and the corresponding eigenspaces are the space spanned by $(1,1,1)$ and its orthogonal complement, respectively) and generate three independent variables with normal distributions with variances given by the diagonal elements.