Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?, 1); (?, 3); (?, 2); (?, 3); (?, 4); (?, 2)}. (i)Deduce the matrix of the complementary relation, ?? ?, clearly outline and comment on your result. (ii) A relation T is defined on the set Y above from Y to Y as ? = {(1,1); (4,2); (1,3); (2,4); (2,1); (3,2); (3,3); (3,4); (1,2); (2,3); (4,4); (4,1)}, compute and analyze ? ??? −1 . (b) Given the functions f and g de defined by ?(?) = 6?+5 7?−5 , ? ≠ 5 7 ; ??? ?(?) = 2? 2 − 3? + 4. Critically analyze and deduce the formula defining the (i) composition function gof (ii) inverse function ? −1 (c)Apply the Runge-Kutta formula as a tool for solving and analyzing numerical differential equation, critically compute and analyze the numerical solution of ? ′ = ?(?, ?) = 1 + ? 2 , y(0) = 0. Computing for the first step, with ℎ = 0.5
Consider the relation R defined on the set X={a,b,c,d} and
Y={1,2,3,4} from X to Y, where R=
{(?, 1); (?, 3); (?, 2); (?, 3); (?, 4); (?, 2)}.
(i)Deduce the matrix of the complementary relation, ??
?, clearly
outline and comment on your result.
(ii) A relation T is defined on the set Y above from Y to Y as ? =
{(1,1); (4,2); (1,3); (2,4); (2,1); (3,2); (3,3); (3,4); (1,2); (2,3); (4,4); (4,1)},
compute and analyze ?
???
−1
.
(b) Given the functions f and g de defined by ?(?) =
6?+5
7?−5
, ? ≠
5
7
; ??? ?(?) = 2?
2 − 3? + 4. Critically analyze and deduce the formula
defining the
(i) composition function gof
(ii) inverse function ?
−1
(c)Apply the Runge-Kutta formula as a tool for solving and analyzing numerical
differential equation, critically compute and analyze the numerical
solution
of ?
′ = ?(?, ?) = 1 + ?
2
, y(0) = 0. Computing for the first step, with
ℎ = 0.5
Step by step
Solved in 2 steps
