The Gauss elimination at the second column can be obtained by multiplying to the relation (2) the lower triangular matrix The matricial equation (2) becomes 0, Gn-1Gn_2+++G2G is an invertible matrix and the equation (3) becomes with L = G;'Gz'---G)!,G_", and we have the decomposition of A as product of lower triangular matrix by an upper triangular matrix Example 3 Consider the following two systems of linear equations
