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How do I construct two correlated random variables with correlation $\rho$ given two i.i.d normal r.v.? Do I just multiply the correlation matrix by a vector generated with two i.i.d normal variables?

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    Sorry but I fail to see the reason which prevents you from accepting this answer.2012-07-28

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If $X$ and $Y$ are independent random variables with the same variance, then

$Z = \rho X + \sqrt{1-\rho^2} Y$

is a random variable such that ${\rm Corr}(X,Z)=\rho$.

Additionally, if $X$ and $Y$ are standard normal, then $Z$ is also standard normal.