Find the determinant of the matrix A = \begin{bmatrix} 3 & 5 & -1\ 4 & 0 & 2\ -6 & -3 & 2 \end{bmatrix} by cofactor expansion about one of the row. Find matrix x for AX = B, given A= \begin{bmatrix} 1 & 0 \ -1& 1 \end{bmatri...
By establishing new multiple inverse series relations (with their connection coefficients being given by higher derivatives of fixed multivariate analytic functions), we illustrate a general framework to provide new proofs for MacMahon’s master theorem and the multivariate expansion formula due to Good ...