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This report considers the multivariate linear regression model X = F1 Xi F2 +E, where X is a c x N matrix of observations, F1 is a known c x p matrix of covariates, F2 is a known m x N design matrix (containing values of independent variables in the regression), and XI is an unknown p x m matrix of regression coefficients assumed under a null hypothesis H0 to satisfy a system of linear restraints of the form H0: U1 Xi F3 = ab, where F3: m x k and b: s x h are known matrices, and U1: r x p and alpha: r x s (s or = r or = p) are unknown matrices of restraint coefficients. The error matrix E: c x N is assumed to have columns which are statistically independent, multivariate normal random vectors with common mean vector 0 and common unknown matrix sigma.