3 votes 3 votes The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix. (A) Always true (B) Sometimes true (C) False (D) None of the above Linear Algebra rank-of-matrix matrix linear-algebra engineering-mathematics + – Parshu gate asked Nov 11, 2017 Parshu gate 572 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Satyajeet Singh commented Nov 12, 2017 i edited by Satyajeet Singh Dec 9, 2017 reply Follow Share Here we are given homogenous system of linear equation . That means that RHS side of each equation is 0 Hence the augmented matrix in this case will be nothing but coefficent matrix with a added column with all 0 . This new column being all 0 does not contribute to the rank of the augmented matrix . Hence the rank of coefficient matrix remains equal to the augmented matrix. So the answer will be a) Always true 3 votes 3 votes Mahbub Alam commented Nov 16, 2018 reply Follow Share good explanation 0 votes 0 votes Please log in or register to add a comment.