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

(a)

0

(b)

1

(c)

m

(d)

n

The rank of the matrix  \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is ________.

(a)

0

(b)

1

(c)

2

(d)

3

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

If  \(T=\begin{array}{l} A \\ B \end{array}\left(\begin{array}{ll} 0.7 & 0.3 \\ 0.6 & x \end{array}\right)\) is a transition probability matrix, then the value of x is ________.

(a)

0.2

(b)

0.3

(c)

0.4

(d)

0.7

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