If `|[r+2,5],[-2,r+1]|=|[4,y+3],[z,3]|`, then

[[2,5],[3,4]][[3,1],[-2,3]]=[[x,y],[1,z]] find x,y and z.

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)}

If Delta_r=|[2^(r-1)2 , 3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

If S_r = |[2r,x,n(n+1)],[6r^2-1,y,n^2(2n+3)],[4r^3-2nr,z,n^3(n+1)]| then sum_(r=1)^nS_r does not depend on-

If A={1, 2, 3, 4, 5} and R:ArarrA is {(1,2), (2,3), (4,5), (3,3)} then write R^-1:ArarrA .

If quad cos((2r pi)/(5))+i sin((2r pi)/(5)),r=0,1,2,3,4 then z_(1)z_(2)z_(3)z_(4)z_(5) is equal to ,r=0,1,2,3,4

If A= {x,y,z}, B=(1,2,3} and R= {(x,2),(y,3),(z,1),(z,2), then find R^(-1) .

If Delta_r=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t