4. If we do not discuss orthogonal diagonalization, you may omit this problem. Let A be any m x n matrix. Show that ATA has an orthonormal set of n eigenvectors.

Q: Find the general solution of the DE y" + 4y + 4y = ex

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Q: The given equation is: 0.2x1 + 4x2 - 0.4x3 = 32 0.5x10.2x2 + 2.5x3 = -5.1 7.5x1 + 0.1x2 - 1.5x3 =…

A:

Q: (a) (i) For the finite arithmetic sequence 5, 8, 11,..., 44. write down the first term a, the…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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Q: 6. Find the Laplace transform of the following functions (b) g(t) = te * sinh3t.

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Q: : Find the divergence of the vector field the point (2,4,1). y F(x, y, z) = x² √yi + =j+zk

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Q: Find the local maxima, local minima, and saddle points of the function, f(x,y) = x³ + 3xy + y³

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Q: Q.5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendicular on the plane passer through…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

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Q: Q2:/ By using Z-tansform, solve the recurrence relation Xk+2 + 5xk+1 + 6x = 1 where x = 0 and x₁ = 1

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Q: (d) (i) Factorise the quadratic expression x² + 3x - 28. 22 (ii) Use your answer to part (d) (i) to…

A:

Q: Let a graph have vertices q, r, s, t, u, v and edge set {{q, s}, {r, v}, {s, v}, {t, u}} . On paper,…

A: Given: A graph has vertices q, r, s, t, u, v and edge set q, s, r, v, s, v, t, u. To find: a) Degree…

Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: For the values 2, 4, 6 thee variance is 1.66 2.77 2.11 O 1.33 O 2.66

A: We have to find the variance from the given data.

Q: *).). (a) Show that X is measurable with respect to o-field G if and only if o(X) C G. Show that X…

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Q: 00 Let f(t) be a function on [0, ∞). The Laplace transform of f is the function F defined by the…

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Q: We consider the following differential equations: xy" + xy' - (x − 3) y = 1 pour x > 0. Give the…

A: Consider the following differential equations: xy''+xy'-(x-3)y=1 for x>0   To Find: General form…

Q: 6. Find the Laplace transform of the foll (a) g(t) = et+2+ sint cost+to(t-2 (b) a(t) = te sinh3t.…

A: Introduction:   The Laplace transformation is very significant integral transformation that is used…

Q: show that the following function analytic f(z)= 4e²+ Sin Z arp

A: Explanation of the answer is as follows

Q: Q.4. Use the Ratio Test to determine if the following series converges or diverges. n! (2n+1)!

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Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost + tô(t-2). (b)…

A: Please see the attachment

Q: Q5: Find the general solution for the following second order differential equation: y" - 4y' + 4y =…

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Q: Find the standard matrix of the linear transformation T: R² → R³ given by T(x₁, x2) = (2x₁ - 3x2, x₁…

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Q: 17. A manufacturer can sell a certain health supplement for P1,100 per unit. Its total cost consists…

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Q: 2. For the quadratic function y = -6x² + (K + 4)x+9, find the following: a. The Axis of Symmetry of…

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Q: of the periodic function f(x) given

A: To find- Find the Fourier coefficients of the periodic function fx given below and find the Fourier…

Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: 1 0.3 (ахуг

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Q: d) (x+27) -3 X lim-

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Q: Let f(t) be a function on [0, ∞o). The Laplace transform of f is the function F defined by the…

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Q: A. B● A B D E g с D

A: Option A is the correct answer

Q: Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first…

A: Given function is fx=x2. We have to estimate approximate derivative of the given function at x=1 for…

Q: change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor integral…

A: To change cartesian equation into polar, we use following substitutions x=r cosθy=r sinθdydx=r dr dθ

Q: 1. determine whether the following argument is valid or invalid: (A → B) → (C → D) B → D A → C ∴…

A: We will use a truth table to determine the validity of the arguments. The argument is valid if…

Q: Q.4) (a) Scratch the function X ㅠ - X (0 < x < π). Is it a periodic function? If so what is the…

A: The given problem is to Sketch the given function and to find the period of the give function and…

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Q: [(p^~q) v~r] ^ (q^r)

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Q: Consider the initial-value problem y'= y, y(0) - 7. (a) Use Euler's method with each of the…

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Q: 2. Find the inverse transform of 2s² +5s-6 $³3s2-13s +15

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Q: For the following simplex tableau (a) Compute the next pivot element. (b) Determine the next…

A: Given,

Q: 3. A group of friends are planning a trip through Alberta. They have created a list of communities…

A: Given; It is given that a group of police officers are planning a bike ride in Alberta to raise…

Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2). (b)…

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Q: A phone number in Toronto is a 10-digit number. The first three is an area code which is 416, 905,…

A: Introduction: When we arrange a certain number of objects in a different order, the arrangement is…

Q: (0) Let R be a commutative ring with identity and I be ideal of R. Then I is primary if and only if…

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Q: 1. What is the largest n such that Pʼn is a subgraph of K4? 2. What is the largest n such that Cn is…

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Q: (a) Use sigma notation to write the Maclaurin series for cosлx.

A: Please see the attachment  According to the guidelines we are supposed to do one problem.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.