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3x3 color matching matrix

I am trying to color calibrate a couple of webcameras to a macbeth chart. I have a list of 24 colors from each camera and the macbeth color values. How does one go about finding the solution for the 3x3 color matching matrix (one for each camera) that can be applied to correct the camera colors to match the macbeth. The application of the matrix is casual, how does one determine/solve/create it. Thomas.