multivariate normal transformation

X and Y are bivariate normal with mew 1 = mew 2 = 0 and var 1 = var 2 = 1 and correlation coefficient of rho. Find the distribution of Z = aX + bY (where a and b are non-zero).

I solved this by writing Z as a linear transformation of x and y and then applying the theorem that a transformation of a multivariate normal is also multivariate normal. I just wanted to compare my final answer with the correct solution.

Thanks.

EDIT: FInal solution is:

N2(2x1 zero vector matrix, [a b]' * [1 rho rho 1] * [a b])

Second matrix is 2x2 not sure how to write it...

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You might include your final solution in the question. –  Did Oct 12 '11 at 7:18
You've asked almost 40 questions on this site. It would be beneficial for you and helpful to others to learn just enough $\LaTeX$ to typeset your math. :) –  cardinal Oct 12 '11 at 12:19
Some people would write your matrix [[1,rho][rho,1]] (first line, then second line, and so on). –  Did Oct 14 '11 at 17:47