rank of matrix

Question

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

Comments

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

---

good explanation