Conversion between primary colours Heads up, this is homework.  Just a little stumped :)

I have some arbitrary primaries, A, B, C, which I want to express in terms of the standard XYZ primaries.  

I have that the tristimulus values with respect to the ABC primaries for some random colour R is defined by some linear matrix equation:

$\begin{bmatrix} R_a \\
R_b \\
R_ c \\
\end{bmatrix}
%
= 
%
\begin{bmatrix}
a_{00} &amp; a_{01} &amp; a_{02} \\
a_{10} &amp; a_{11} &amp; a_{12} \\
a_{20} &amp; a_{21} &amp; a_{22}
\end{bmatrix}
%
\begin{bmatrix}
R_x \\
R_y \\
R_z
\end{bmatrix}
$

How can the primaries be computed from this information?
Hint: I think you want to determine the [Rx,Ry,Rz] required to make the left side of your equation look like [1 0 0], [0 1 0], and [0 0 1]. This will get you A,B,C expressed in terms of X,Y,Z.