Application of matrices

If A=( 1 2 3) then the rank of AA^T is -----

• O

• 2

• 3

• 1

The rank of m $\times$  n matrix whose elements are unity is 

• O

• 1

• m

• n

If  $\rho$  (A) =r then which of the  following  is correct? 

• All the  minors of order r which does not vanish

• A has at least  one minor of order r which does not vanish

• A has atleast  one (r+1) order minor which vanish 

• All (r+1) and higher order minors should not vanish

If $\rho$   (A) = $\rho$   (A, B) then the system is

• Consistent and has infinitely many solutions

• Consistent and has a unique solution

• Consistent

• Inconsistent

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

• 2

• 1

• 0

• 3

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

• A unique solution

• No solution

• Infinitely many solutions

• None of these

Cramer's rule is application  only to get an unique  solution  when

•   $\Delta$  Z $\ne$   0

•  $\Delta$  X $\ne$  0

•   $\Delta$  $\ne$   0

•  $\Delta$  Y  $\ne$  0

Rank of null matrix is

• 0

• -1

• $\infty$

• 1

Which of the following is not elementary transformation

• Ri $\leftrightarrow$ Rj

• Ri $\rightarrow$ 2Ri+ 2Cj

• Ri $\rightarrow$ 2Ri -4Rj

• Ci $\rightarrow$ Ci+5Cj

If T= A.   0.7   0.3
         B    0.6   x       is a Transition  probability  matrix 
Then the value of x is

• 0.2

• 0.3

• 0.4

• 0.7