Let Xn be the Markov chain with states S = {1, 2, 3, 4} and transition matrix.

a.) Let X0 = 3 and let T3 be the first time that the Markov chain returns 3, compute P(T3 = 2 given X0=3). Please show all work and all steps.

b.) Find the stationary distribution π. Please show all work and all steps.

for the system equation of x' = Ax   if Coefficients Matrix A be ? = [ 5 −5 −5 −1 4 2 3 −5 −3 ] , find the basic matrix

a) Solve the Cauchy-Euler equation: x^2y'' - xy' + y = x^3

b) Solve the initial-value problem: y'' + y = sec^3(x); y(0) = 1, y'(0) =1/2

Gaus-Jordan Elimination:

A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbohydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two slices of whole-grain bread supply 2.2 mg of iron, 10 g of protein, and 12 g of carbohydrates. If a person on a special diet must have 22.9 mg of iron, 173.5 g of protein, and 131 g of carbohydrates, how many glasses of skim milk, how many quarter-pound servings of meat, and how many two-slice servings of whole-grain bread will supply this?

Find the 0-divisors of the following rings. (a) Z2 × Z4

(b) Z91

(c) Z167

Consider the following real 3rd order polynomial

f (x)= x^3− 5.5 x^2− 5x+ 37.5

A) Use the bisection method to determine one of the roots, employing initial guesses of xl = - 10, xu = -1, and a stopping criterion εs=12% .

B) Use the false position method to determine a root, employing initial guesses of xl = - 1, xu = 4, and a stopping criterion εs=3%. Was this method the best for these initial guesses?

C) Use the fixed point iteration to determine a root, employing an initial guess x0 = 7 and a stopping criterion εs=5%

D) Use the Newton-Raphson to determine a root, employing an initial guess x0 = 7 and a stopping criterion εs=5%

Please please show all steps

Thank you

Solve the linear programming problem by the method of corners.

Find the minimum and maximum of P = 4x + 2y subject to

The minimum is P =  

at (x, y) =

The maximum is P =  

at (x, y) =

Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m, n) ∈ R if and only if m + n = 2k for some integer k. For example, (3, 11) is in R because 3 + 11 = 14 = 2(7).

(a) Is the relation reflexive? Prove or disprove.

(b) Is the relation symmetric? Prove or disprove.

(c) Is the relation transitive? Prove or disprove.

(d) Is it an equivalence relation? Explain.

Find the minimizer of f(x) = x⁴ - 14x³ + 60x² - 70x on interval [5, 7] using the golden section method with uncertainty 0.2.

Hello.

Linear Algebra class.

In a linear system of equations, the solution is one of the possibilities.

1)there is one unique solution(only one) which means the line of the equation interest only one time at a point.

2)there are many solutions (infinity) if the lines of equations lie on one another.

3)there is no solution if the line of the equation are parallel.

how to test for each possibility WITHOUT graphing the system of equations using the coefficients in each equation as well as the signs?

Thank you

Problem 2

Find the locations and values for the maximum and minimum of f (x, y) = 3x^3 − 2x^2 + y^2 over the region given by x^2 + y^2 ≤ 1.

and then over the region x^2 + 2y^2 ≤ 1.

Use the outline:

INSIDE

Critical points inside the region.

BOUNDARY

For each part of the boundary you should have:

• The function g(x, y) and ∇g

• The equation ∇f = λ∇g
• The set of three equations in three unknowns and their complete solution set

• The list of endpoints of that boundary component (if necessary)

COMPARE

Finally, you compute the value of f(x,y) at each point you have identified and compare to find the minimum and maximum.

Please show all steps for a thumbs up, thank you!

Lay out the design for two between-subjects experiments: a) an experiment involving an experimental group and a control group, and b) a factorial design with three independent variables that have three, and two levels respectively.

Find eigenvalue (?) and eigenfunction and evaluate orthogonality from the given boundary value problem. ?2?′′ + ??′ + ?? = 0, ?(1) = 0, ?(5) = 0. Hint: Use Cauchy-Euler Equation, (textbook pp141-143).