Answer to Question #54791 in Abstract Algebra for Joseph

Question

Given a set X={a,b,c}, and a function Ψ:X→X define by Ψ(a)=b,Ψ(b)=a,Ψ(c)=c
. the function is (a)Only unto (b) only injective (c) bijective (d)no solution
A matrix X=(35 12 ) define a function from R 2 toR 2 by f X (a,b)=(3a+b,5a+2b) . find the inverse function of f X (a)f −1 X (a,b)=(3a−b,−5a+3b) (b)f 1 X (a,b)=(2a−b,−5a+3b) (c)f 5 X (a,b)=(2a−b,−5a+3b) (d) f 1 X (a,b)=(2a−b,−5a+4b)
Which of the following is divisible by 17 for all positive integer n (a) 7 n +2 (b) 6 n +2 (c) 2.7 n +3.5 n −5 (d)3.5 2n+1 +2 3n+1