in Linear Algebra
448 views
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
in Linear Algebra
448 views

2 Comments

edited by
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
3
good explanation
0
0

Please log in or register to answer this question.

Related questions