The transformation from the RGB primaries of a television monitor to the CIE XYZ color notation system is usually formulated as a three by three matrix applied to a one by three vector. In the general case, however, this is not true because the black point of the monitor gamut is displaced from the origin of CIE XYZ space. An affine transformation is necessary to accomodate this translation of the monitor gamut, and this affine transformation can be reformulated as a four by three matrix times a one by four vector. Balancing the monitor guns so that they maintain the same luminance ratio over their entire dynamic range can minimize the error of assuming a three by three transform when a four by three matrix is actually called for. This procedure also leads to improved calibration for applications where the front panel brightness and contrast controls will be adjusted. The technique of balancing the monitor guns has been employed in the broadcast television industry for many years. This paper presents the theory to support the validity of this approach. First, the affine transformation that is necessary to fully characterize the RGB to CIE XYZ transformtion is developed. Next, colorimetric errors are identified for balanced and unbalanced monitors when the assumption of a simple three by three matrix transform is made. Finally, the effect on both balanced and unbalanced monitor gamuts of adjusting the front panel brightness and contrast controls is discussed.