Let S= A= ( array lll 0 & 1 & c 1 & a & d 1 & b & e array ): a, b, c, d, e 0,1 . and .|A| -1,1 , where |A| denotes the determinant of A . Then the number of elements in S is

Step-by-step solution

(|A|=-(e-d)+c(b-a)= 1 ) Case (i) : (c=0 (e, d)=(1,0),(0,1) 2 ) ways b and a can be each 2 ways ( ) Total (=8 ) ways Case (ii) : (c 0 c=1 ) ( d-e+b-a= 1 ) ( . array llll 1 & 1 & 1 & 0 1 & 1 & 0 & 1 0 & 0 & 1 & 0 0 & 0 & 0 & 1 array 4 2=8 ) ways Total (=16 ) ways