Find minors and cofactors of the elements `a_11 ,a_21 `in the determinant ` Delta= {:[( a_11,a_12,a_13),( a_21,a_22,a_23),( a_31,a_32,a_33) ]:}`

Let S = {1,2,3}. Determine whether the functions f : S to S defined as below have inverses. Find f ^(-1), if it exists. (a) f = {(1,1), (2,2), (3,3)} (b) f = {(1,2), (2,1),(3,1)} (c ) f { (1,3), (2,3),(2,1)}

The marks obtained by 35 students in a test in statistics (out of 50) are as below. {:(35,1,15,35,45,23,31,40,21,13,15),(20,47,48,42,34,43,45,33,37,11,13),(27,18,12,37,39,38,16,13,18,5,41),(47,43, , , , , , , , ,):} Construct a frequency distribution table with equal class intervals, one of them being 10-20 (20 is not included).

Given below are the ages of 45 people in a colony. {:(33,8,7,25,31,26,5,50,25,48,56),(33,28,22,15,62,59,16,14,19,24,35),(26,9,12,46,15,42,63,32,5,22,11),(42,23,52,58,62,10,24,43,51,37,48):} 36 Construct grouped frequency distribution for the given data with 6 class intervals.