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) ]:}`

Find minors and cofactors of the elements of the determinant {:[( 2,-3,5),( 6,0,4),( 1,5,-7)]:} and verify that a_11 A_31+ a_12A_32+a_13A_33=0

Let A=[a_("ij")]_(3xx3) be a matrix such that A A^(T)=4I and a_("ij")+2c_("ij")=0 , where C_("ij") is the cofactor of a_("ij") and I is the unit matrix of order 3. |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then the value of lambda is

If Delta = {:[( a_11, a_12, a_13),( a_21,a_22,a_23) ,(a_31,a_32, a_33) ]:} and is Cofactors of a_ij then value of Delta is given by

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 A = [{:(3," "1,-1),(2,-2," "0),(1," "2,-1):}] "and"" "A^(-1)=[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))] then the value of a_(23) is

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)}

If X = {1,2,3,4,5}, Y = {1,3,5,7,9} determins which of the following relations from X to Y are functions ? Give reasonfor your answer. If it is a function. State its type. (i) R_(1) = {(x,y) | y = x + 2, x in X , y in Y } (ii) R_(2) = {(1,1),(2,1),(3,3),(4,3),(5,5)} (iii) R_(3) { (1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4) {(1,3),(2,5),(4,7),(5,9),(3,1)}

Let X = { 1,2,3,4 } and R = { (1,1), (1,2),(1,3),(2,2), (3,3),(2,1),(3,1),(1,4),(4,1)}. Then R is