For a matrix A of rank r (A) rank `(A\')ltr` (B) rank `(A\')=r . (C)` rank `(A\')gtr` (D) none of these

If A is an invertible matrix and B is a matrix then (A) rank (AB)=rank(B) (B) rank (AB)=rank(A) (C) rank (AB)gtrank(B) (D) rank (AB)gtrank(A)

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) rltmin{m,n} (B) rlemin{m,n} (C) r=min{m,n} (D) none of these

For a non singular matrix A of order n the rank of A is (A) less than n (B) equal to n (C) greater than n (D) none of these

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemin{m,n} (C) rltmin{m,n} (D) none of these

Let A be a matrix of rank r. Then,

For a matrix A of order 3xx3 where A=[(1,4,5),(k,8,8k-6),(1+k^2, 8k+4, 2k+21)] (A) rank of A=2 for k=-1 (B) rank of A=1 for k=-1 (C) rank of A=2 for k=2 (D) rank of A=1 for k=2

The rank of a null matrix is

Thirty two players ranked 1 to 32 are playing is a knockout tournament. Assume that in every match between any two players, the better ranked player wins the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is (A) 16/31 (B) 1/2 (C) 17/31 (D) none of these

Thirty two players ranked 1 to 32 are playing is a knockout tournament. Assume that in every match between any two players, the better ranked player wins the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is (A) 16/31 (B) 1/2 (C) 17/31 (D) none of these

Rank of a non zero matrix is always (A) 0 (B) 1 (C) gt1 (D) gt0