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 A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.

If Delta = {:|( a_11, a_12, a_113),( a_21,a_22,a_23) ,(a_31,a_32, a_33) |:} and Aij is Cofactors of a_ij then value of Delta is given by

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not ? (i) R={(4,1),(5,1),(6,7)} (ii) R={(2,3),(2,5),(3,3),(6,6)} (iii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (iv) R={(1,1),(2,1),(3,1),(4,1),(5,1)}

Let A = {1,2,3,4} and R be a relation in A given by R = {(1,1) (2,2) (3,3) (4,4) (1,2) (2,1) (3,1) (1,3)} . Then R is

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)}

{:|( 2,-3,5),( 6,0,4),( 1,5,-7)|:} verify that a_11 A_31+ a_12A_32+a_13A_33=0

On set A={1,2,3}, relations R and S are given by R={(1,1),(2,2),(3,3),(1,2),(2,1)}, S={(1,1),(2,2),(3,3),(1,3),(3,1)}. Then

If [(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))]=[(1,2,3),(2,3,4),(3,4,5)][(-1,-2),(-2,0),(0,-4)][(-4,-5,-6),(0,0,1)] , then the value of a_(22) is -

Let the functions f and g be defined by, f={(1,2),(3,-2),(-1,1)} and g={(2,3),(-2,1),(1,3)} Prove that , (g o f) and ( f o g) are both defined . Also find (g o f) and (f o g) as sets of ordered pairs.