Which of the following is false? 1. If (A ) is a skew symmetric matrix of order (5 5 ), then the rank of (A ) is less than 5. 2. If (P ) is a non-zero column matrix and (Q ) is a non-zero row matrix, then the rank of (P Q ) is 1 3. Rank of ( [ array lll 1 & 2 & 3 2 & 3 & 4 5 & 6 & 7 array ] ) is 2 4. If the lines (a_r x+b_r y+c_r=0(r=1,2,3) ) are distinct and intersect at a point, then ( rank ) of ( [ array lll a₁ &

Step-by-step solution

The skew-symmetric matrix of order (5 5 ), has rank less than 5 because determinant of odd ordered skew symmetric matrix is zero. If (P ) is a non-zero column matrix and (Q ) is a non-zero row matrix, then (P Q ) is a matrix of order (1 1 ), so rank of matrix (P Q ) is one. Since, the ( | array lll 1 & 2 & 3 2 & 3 & 4 5 & 6 & 7 array |=1(21-24)-2(14-20)+3(12-15) ) (=-3+12-9=0 ) and there is no cofactor of any elements is zero, so rank is 2. If the lines (a_r x+b_r y+c_r=0,(r=1,2,3) ) are distinct and intersect at a