Question

In **GF(2 ^{4}),** derive the multiplicative
inverse of

Answer #1

plzzz rate

Determine the multiplicative inverse of x3 +
x2 + 1 in GF(24), using the prime (irreducible)
polynomial m(x) = x4 + x + 1 as the modulo polynomial.
(Hint: Adapt the Extended Euclid’s GCD algorithm, Modular
Arithmetic, to polynomials.)

a. Show that if a has a multiplicative inverse modulo N,then
this inverse is unique (modulo N).
b. How many integers modulo 113 have inverses? (Note: 113 =
1331.)
c. Show that if a ≡ b (mod N) and if M divides N then a ≡b (mod
M).

Use extended Euclid algorithm to find the multiplicative inverse
of 27 modulo n, if it exists, for n = 1033 and 1035. Show the
details of computations.

We say that x is the inverse of a, modulo n, if ax is congruent
to 1 (mod n). Use this definition to find the inverse, modulo 13,
of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Show by example that when the modulus
is composite, that not every number has an inverse.

Given the function h(x)= x4+2x3-13x2-14x+24 find the zeros given
that x =1 is a zero. Please show your work!!

Use polynomial long division to divide p(x) = x4 -
3x3 + x - 1 by x2 + x - 3

Given f(x) = , f′(x) = and f′′(x) = , find all possible
x2 x3 x4
intercepts, asymptotes, relative extrema (both x and y values),
intervals of increase or decrease,
concavity and inflection points (both x and y values). Use these
to sketch the graph of f(x) = 20(x − 2)
.
x2

Consider the utility function U(x1,x2) = ln(x1) +x2. Demand for
good 1 is: •x∗1=p2p1 if m≥p2 •x∗1=mp1 if m < p2 Demand for good
2 is: •x∗2=mp2−1 if m≥p2 •x∗2= 0 if m < p2 (a) Is good 1
Ordinary or Giffen? Draw the demand curve and solve for the inverse
demand curve. (b) Is good 2 Ordinary or Giffen? Draw the demand
curve and solve for the inverse demand curve. (c) Is good 1 Normal
or Inferior? Derive and...

1. (a) Construct a Pearson’s χ 2 test for H0 : (X1, X2, X3, X4)
has multinomial distribution with parameters (θ1, 3θ1, θ2, 1 − 4θ1
− θ2) against HA : (X1, X2, X3, X4) has some other multinomial
distribution, at the significance level α = 0.05. (b) Apply the
test in (a) to the data X = (26, 52, 34, 18

Derive the inverse kinematics for a two-link planar robot, given
(x, y) coordinate....

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