The rank of m x n matrix whose elements are unity is ________.

(a)

0

(b)

1

(c)

m

(d)

n

The rank of the unit matrix of order n is ________.

(a)

n −1

(b)

n

(c)

n +1

(d)

n²

If A =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^T is ________.

(a)

0

(b)

1

(c)

2

(d)

3

The rank of the diagonal matrix\(\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right) \)

(a)

0

(b)

2

(c)

3

(d)

5

In a transition probability matrix, all the entries are greater than or equal to _______.

(a)

2

(b)

1

(c)

0

(d)

3

The system of equations 4x + 6y = 5, 6x + 9y = 7 has _______.

(a)

a unique solution

(b)

no solution

(c)

infinitely many solutions

(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)

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

The rank of an n x n matrix each of whose elements is 2 is __________

(a)

1

(b)

2

(c)

n

(d)

n²

If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

(a)

3

(b)

± 3

(c)

± 6

(d)

6

If A, B are two n x n non-singular matrices, then ___________

(a)

AB is non-singular

(b)

AB is singular

(c)

(AB)^-1 = A^-1 B^-1

(d)

(AB)^-1 does not exit