 In theorem 3 here, we suppose that x is a random variable with multivariate normal with mean vector mu and variance covariance matrix sigma, then y equals to cx plus t, where c is a q into p matrix and d is the q into 1 vector is distributed as this one. Here also we have a transformation, which transformation is linear transformation we have taken. In univariate case what you have is y equals to ax plus b in univariate, so here x, x is follows the univariate normal distribution with mean mu and variance sigma square, okay because we have taken linear in it, then y, this y is also follows the normal with mean, what is mean of this, mu plus b and its variance a square sigma square, this is what we have in univariate case, we have done linear transformation, so here also we are taking linear transformation here, this is the linear transformation, this is the mean vector and this is the variance covariance matrix, so we have the probability density function of the multivariate normal distribution, journal you have pdf of multivariate normal distribution under the transformation, now here you have a transformation, under the transformation we need x value, x value we have found y minus d, so x which is equals to c inverse y minus d, okay, then we have found Jacobian, Jacobian you have mod of c determinant of inverse, the pdf of y, now pdf of y which is transformed variable, what we have is pdf of value as it is, now here you have x, we have evaluated the place of x, x minus mu minus into x minus mu, here you see x minus mu transpose, so this transpose here, x minus mu transpose sigma inverse, this is the x minus mu and the Jacobian, multiply the Jacobian derivative of it, so after this simplification we have simplified it further because it has transpose, we have simplified it and we have mod of, that is the value of the Jacobian we have found, we have entered that value, this simplification is done, we have done this simplification many times, that is why I am not repeating it, you have simplified all these values in this simplification, c plus mu y minus this, mod y minus this, determinant, you have got this value, the value of sigma, we have written further, density function of a random vector of the multivariate normal with mean vector, this and variance covariance matrix, this, you have got this x minus mu as y minus mu, so mean vector and this is the variance covariance matrix, hence if x is the multivariate normal distribution, then the transformed variable also follows the multivariate normal distribution, here we have the place of x, transformed variable also follows the multivariate normal distribution with mean vector, with parameter mean and the variance covariance matrix.