Given vector s = [4, -5, 7], u = [-6, 8, 11], and v = [-5, 3, -7]
a. Let r1(t) be the vector equation through s and u. Express the vector equation r(t) in two ways and then find r(1); r(-5); r(9)
b. Let r2(t) be the vector equation through u and parallel to r1(t), Express r2(t) in two forms and then find r(-3); r(13); r(2)
c. Let w = 2s -4v, find r(t) through u and v

Prove the follwing statements

Suppose that S is a linearly independent set of vectors in the vector space V and let w be a vector of V that is not in S. Then the set obtained from S by adding w to S is linearly independent in V.

If U is a subspace of a vector space V and dim(U)=dim(V), then U=V.

Create your own 2 × 2 payoff matrix for a two-person zero-sum game with v − < v+. Solve your game (find a saddle point and the value of the game).

In matlab ask the user to select whether to repeat the Newton-Raphson calculation or end the program. If the user exits out of the menu, repeat the request until the user makes a selection. If the program is repeated, store the new final value of the root and new number of iterations in the same variables without overwriting the previous results. Once the user chooses to end the program, save the variables containing the root values and numbers of iterations as calculation res.mat

this is my code so far

vector = input("Enter a vector which has an even number of elements: ");

the vector you enter is the polynomial you work with

the vector that is entered is [0.2 0.3 0 2.4 9.8 -21.4]

(a) Let G be a finite abelian group and p prime with p | | G |. Show that there is only one p - Sylow subgroup of G. b) Find all p - Sylow subgroups of (Z₂₅₀₀, +)

What are the five forces of Porter's model? What are the specific elements that should be assessed under each of Porter's five forces? What is the difference between the company you are evaluating, the country industry and the global industry? What is the purpose of the Competitor Profile Matrix? What are different key success factors that a company would consider? What is the purpose of completing a partial SWOT (OT)? From where did the factors of the EFE matrix derive

Find the Fourier coefficients of the following signal.

x(t) = 5 + 2sin(w0.t) + cos(2.w0.t) - 3sin(2.w0.t)

(1 point)

Suppose that

R1={(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)},R1={(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)},
R2={(1,1), (1,2), (2,1), (2,2), (3,3), (4,4)},R2={(1,1), (1,2), (2,1), (2,2), (3,3), (4,4)},
R3={(2,4), (4,2)}R3={(2,4), (4,2)} ,
R4={(1,2), (2,3), (3,4)}R4={(1,2), (2,3), (3,4)},
R5={(1,1), (2,2), (3,3), (4,4)},R5={(1,1), (2,2), (3,3), (4,4)},
R6={(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)},R6={(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)},

Determine which of these statements are correct.
Check ALL the correct answers below.

A. R3R3 is transitive
B. R2R2 is not transitive
C. R3R3 is reflexive
D. R5R5 is transitive
E. R5R5 is not reflexive
F. R4R4 is antisymmetric  
G. R6R6 is symmetric
H. R1R1 is not symmetric  
I. R1R1 is reflexive
J. R2R2 is reflexive  
K. R3R3 is symmetric
L. R4R4 is transitive
M. R4R4 is symmetric

Expand the function f(z) = 1 / (z + 1)(z − 3)

as a Laurent series about z = 0 in three regions: 1) |z| < 1, 2) 1 < |z| < 3 and 3) |z| > 3.

Decide, with justification, if the following set properties are true for any sets A, B, and C.

1. A∪(B∩C)⊆A.

2. A∪(B∩C)⊆B.

3. A ∩ B ⊆ A

4. B ⊆ A ∪ B
5. A ⊆ B ⇒ A ∪ B ⊆ B.

6. A ∪ B ⊆ B ⇒ A ⊆ B.

7. A⊆B⇒A∩B=A.

8. A ∩ B = A ⇒ A ⊆ B
9. A∩(B∪C)⊆A∪(B∩C)
10. A∪(B∩C)⊆A∩(B∪C)
11. A\(B∩C)=(A\B)∪(A\C)

How do we construct the Ito's Integral(also called the stochastic integral), and what are the properties of the integral?

Define the following predicates:

Real( x)   =   “x is a real number”.

Pos(x) =   “x is a positive real number.”

Neg(x) =   “x is a negative real number.”

Int(x) =   “x is an integer.”

Rewrite the following statements without using quantifiers. Determine which

statements are true or false and justify your answer as best you can.

a) Pos(0)

b) ∀x, Real(x) ∧ Neg(x) → Pos(−x)

c) ∀x, Int(x) → Real(x)

d) ∃x such that Real(x) ∧∼ Int(x)

1. Show the 4-quadrant position and then find the magnitude and angle of each of the following complex numbers: (12 Points)

(a) 3+j4 (b) -3+j4 (c) -3-j4 (d) 3-j4

A mass weighing 16 pounds stretches a spring

feet. The mass is initially released from rest from a point 5 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to

the instantaneous velocity. Find the equation of motion

x(t)

if the mass is driven by an external force equal to

f(t) = 20 cos(3t).

(Use

g = 32 ft/s²

for the acceleration due to gravity.)

Consider the permutation ρ = (1, 2, 6)(3, 4, 5) in S10. How many conjugates does ρ has in S10? Hence determine the order of Cρ(S10), the centralizer of ρ in S10. Now determine the order of Cρ(A10) by observing that there is an odd permutation in Cρ(S10). How many conjugates does ρ has as an element of A10?