Inserting matrices into equations

I've been trying to create vector equations, ie something like

[matrix1] = [matrix2] [matrix3]

and am completely stumped. (matrix1 and 3 are 1 x 3 and matrix2 is 3 x 3)

I've creating the matrices using bmatrix, but no matter what I do they can't play nice. I've tried surrounding them with \begin{equation}...\end{equation}, $$..$$, and \[ ... \] and everytime I can get two matrices on the same line before Latex generates an error. I add each bit piece by piece but by the third matrix Latex complains about a missing $ needing to be inserted, and when I take out the offending bit it still won't compile and the whole equation needs to be deleted.

It would be great if I can get them with an equation number too.

What should I do to achieve this?

Here are my three matrices:

Code:

`\begin{bmatrix}`

Y \\ I \\ Q

\end{bmatrix}

Code:

`\begin{bmatrix}`

0.299 & 0.587 & 0.114 \\

0.596 & -0.274 & -0.322 \\

0.211 & -0.523 & 0.312

\end{bmatrix}

Code:

`\begin{bmatrix}`

R \\ G \\ B

\end{bmatrix}