If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

consistent

(d)

inconsistent

If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when _______.

(a)

\(\rho (A)=\rho (A,B)>n\)

(b)

\(\rho(A)=\rho(A, B)=n\)

(c)

\(\rho (A)=\rho (A,B) < n\)

(d)

none of these

If \(\left| A \right| \neq 0,\) then A is _______.

(a)

non-singular matrix

(b)

singular matrix

(c)

zero matrix

(d)

none of these

Cramer’s rule is applicable only to get an unique solution when _______.

(a)

\({ \triangle }_{ z }\neq 0\)

(b)

\({ \triangle }_{ x }\neq 0\)

(c)

\({ \triangle } \neq 0\)

(d)

\({ \triangle }_{ y }\neq 0\)

Rank of a null matrix is _______.

(a)

0

(b)

-1

(c)

\(\infty \)

(d)

1