Write one a MATLAB function that implements the Bisection method, Newton’s method and Secant Method (all in one function). Your function must have the following signature

function output = solve(f,options)

% your code here

end

where

the input is

• • f: the function in f(x) =0.
  • options: is a struct type with the following fields o method: bisection, newton or secant
  • tol: the tolerance for stopping the iterations.
  • maximum_iterations: the maximum number of iterations allowed.
  • initial_guess: that is P_0; if the method needs it
  • df: the derivative of f if the method needs it
  • initial_interval: if the method needs it

the output is also a struct type with the following fields

• • message: either ‘success’ or an error message.
• • root: the solution in case of success.
• • iterations: an array that saves all iterations of the algorithm. Each row represents an iteration of the algorithm. Each row must contain P_n, f(P_n) and |P_n-P_n-1|.
• Write a script file that tests your function using the following equations

                                  600x^4 – 550x^3 +200x^2 – 20x -1 = 0

A) Find Eigen values and Eigen vectors for the matrix below.

A = ( 2 3 ; 1 5 ) this is a 2x2 matrix with 2 3 on the first row and 1 5 on the second row

(B) Write down the spectral decomposition of the matrix A.

(C) Is the matrix A positive definite matrix? Why?

5. Determine if the following sets along with the given operations form groups. If so, determine the identity element and whether or not they are Abelian. If not, explain why.

(a) GL(n, Z) where ∗ is matrix multiplication. This is the collection of all n × n nonsingular matrices with integral entries.

(b) Sym(X) where X is a nonempty set and f ∈ Sym(X) if and only if f : X → X is bijective where ∗ is composition.

(c) Aff(1, R), where Aff(1, R) := {fa,b : R → R : fa,b(x) = ax + b, a, b ∈ R, a 6= 0} and ∗ is composition. These are called the one-dimensional affine functions. What happens if we allow a = 0?

(d) T := {z ∈ C : |z| = 1} where ∗ is complex multiplication. We will again encounter T in later sections.

(e) SL(2, Z) where A ∈ SL(2, Z) if and only if A is a 2 × 2 matrix of integers for which det A = 1. What about SL(n, Z) where n ∈ N?

Prove the case involving ∨E of the inductive step of the (strong) soundness theorem for natural deduction in classical propositional logic. Hint: you need to simultaneously consider 3 different instances of entailment, 1 regular and 2 featuring the transformation of an assumption into a premise

there are three brands you can choose; H&M, Banana, and Zara. H&M and Banana clothes cost 100 dollars each and Zara clothes cost 200 dollars each.

How many different purchases can you make if you have to spend 1500 dollars and

must buy AT LEAST (NOT EQUAL) as many H&M clothes as Banana clothes?

1) Use dimensional analysis to find a relationship between the force of the wind, F, on a car. You will also need the velocity, v, the surface area of the car, A and the density of air, p.
.
2) Consider the problem of determining the terminal velocity of a raindrop falling from a motionless cloud. Determine a general model using dimensional analysis. Hint: You will need 5 parameters

Let M be the integer corresponding to the first letter of your last name. For example, if your last name begins with "A", M=1 and if your last name begins with "Z", M=26.

Let k=1/M and consider the logistic equation dy/dt = k y (M - y).

Construct a single figure including

1. Title "Logistic Equation Slope Field and Euler's Method solutions by FirstName LastName" with your actual first and last names, along the top
2. Labels for the axes
3. a slope field for -3 ≤ t ≤ 3, -M/2 ≤ y ≤ 3M/2
4. Euler's method solutions for initial conditions   y(0)=5M/4, y(0)=M, y(0)=M/2, y(0)=0 and y(0)=-M/4, in each case for -3 ≤ t ≤ 3, h=0.1
5. For each initial condition, a label "y(0) = (value)" but with the actual value, at an appropriate location
6. For each solution curve, a label "y(3) ≈ (Euler's method value)" but with the actual value, or "y(3) = ?", at an appropriate location

Print on 8.5x11 paper in landscape format.

First letter of my last name is P.

there are three brands you can choose; H&M, Banana, and Zara. H&M and Banana clothes cost 100 dollars each and Zara clothes cost 200 dollars each.

How many different purchases can you make if you have to spend 1500 dollars and

must buy AT LEAST (NOT EQUAL) as many H&M clothes as Banana clothes?

Suppose that A is an n × n matrix satisfying A3 - 3A + 2A-3l = 0.

Show that A is invertible by the definition of invertible. (Hint: Review the definition of invertible, and then describe the inverse in terms of the matrix A - you don’t need to know what A is to answer this question.)

Let P be a finite p-group. Show that Φ(P) is the unique normal subgroup of P minimal such that the corresponding factor group is elementry abelian

How many ways can you distribute 1 piece of chocolate, 2 licorice sticks, and 7 pixie sticks to 5 children so that each child has exactly 2 pieces of candy?

Given a matrix that defines a reflection about a line, find an equation for this line.

Given a matrix that defines an orthogonal projection onto a line, find an equation for this line.

Could yall give me an example of these questions. And solve it for me.

A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. (Round your answers up to the nearest integer.)

(a) What sample size is necessary if the 95% CI for p is to have a width of at most 0.15 irrespective of p?

(b) If the legislator has strong reason to believe that at least 7/8 of the electorate know of her position, how large a sample size would you recommend to maintain a width of at most 0.15?

Solve the following logic problems. Remember, everyone you meet is either a knight or a knave, knights make true statements, and knaves make false statements. Give your reasoning for each problem. p,q,r and T/F truth table format.

You meet two residents, Alex and Bill. They say the following: Alex: I’m a knight. Bill: Alex is a knight, but I’m a knave. Is Alex a knight or a knave? Is Bill a knight or a knave?

You meet Clara and Davis, who are all like: Clara: One of us is a knight and the other is a knave. Davis: Clara is a knave. Is Clara a knight or a knave? Is Davis a knight or a knave?

You meet Edith and Frank, though only Edith speaks. Edith: Both Frank and I are knaves. Is Edith a knight or a knave? Is Frank a knight or a knave? (Note: Frank’s silence gives no indication of his type, but you can figure out from Edith’s statement.)

You meet Gina, Herbert, and Ichabod. Gina: Ichabod is a knave, if and only if I’m a knight. Herbert: Ichabod is a knight, if and only if I’m a knave. Ichabod: I like pudding. Does Ichabod like pudding?

How to transform x^2+xy+y^2+4x+2y=0 into the standard for of an ellipse and finding the vertices of both major and minor axis. Plot points and graph the ellipse.