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Q: = Use spectral decomposition to orthogonally diagonalize the matrix A [] -7 24 7 24

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Q: Consider the following nonhomogeneous system. X'= - - (-3-³) × + (-4²) Find the eigenvalues of the…

A: We solve given system of DE.

Q: 1.1 Let {fn (2)} = {1 NI +nz ,z ER and 2 > 0. 1.1.1 Find the pointwise limit of the sequence {fn(x)}…

A: To Examine: The series of function Sn(x)=∑k=1∞xk-1 converges uniformly on [-a,a], a∈(0,1) or not.

Q: A Surface Aren S= S2x $ (v)√1-gin + 1-1/₂ = ² "2² (6² - y²) => y=b √4₂²2²-2² 62 S= D SER SUTH (FWD)…

A: From the above details we have,

Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…

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Q: Let C be the code given by the matrix 0 1 1 Suppose x = (11010) and y = (10110)t are received.…

A: If G is a matrix, it generates the codewords of a linear code C by {\displaystyle w=sG} where w is…

Q: Question #3*: Let the matrices A₁, A₂ and A3 be such that: 2 3 4-4-4-4-[9] A₂ = -1 5 A₁ 2 -1 3 -2 A3…

A: Given Matrix is  A1=2-13-2 Solution a) A1-λI=0⇒2-λ-13-2-λ=0⇒2-λ-2-λ+3=0⇒λ2-1=0⇒λ=±1 λ=±1 are the…

Q: 4. T(n) = 4T() + n 5. T(n) = 7T()+n²

A: We use here, Master's Theorem

Q: • f(0) = 1 ● lim f(x) = lim_ƒ(x) = 0 x →∞ x118 • The values of f'(x) and ƒ"(x) are as follows: f'(x)…

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Q: (b) Prove or disprove: If A and B are compact sets, then AB is compact. Q(3) Let g(x): (R,|) →…

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

Q: Find the maximum value of integral over a simple closed curve in a plane oriented counterclockwise…

A: Given,             F→=9xy2i^+4z-9xy2j^+5y-3x2yk^ and C is a simple closed curve in the plane…

Q: Find the solution to the initial value problem: dy = 5y dx y(x) = y(1) = 1

A: Introduction The initial value problem is solved using various techniques. In this question, the…

Q: Determine the Fourier Series in magnitude-phase form of the following periodic functions whose graph…

A: As per company guidelines we can solve one question at a time so i am solving first one. please…

Q: • Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A:

Q: Integrate f (x,y,₁/2) = 2² +12y +7 over the cuna 7 (t) = (²1 +31²) + (1², 1st sz - 6+² try to sketch…

A:

Q: - 31. (2x-y) dx + (4x + y − 3) dy = 0 32. (2x-y+4) dx + (x-2y-2) dy = 0 I In Problems 33-40 solve…

A:

Q: Find a differential equation whose general solution is 8t y = c₁e³t+c₂e-2t

A: We have to find the differential equation whose general solution is given as ;             y = c1e8t…

Q: Michael, Clarissa, Reggie, and Ellen are attending Florida State University (FSU).  One student is…

A: According to the given information, four students Clarissa, Reggie, Ellen and Michael are studying…

Q: Solve the given initial-value problem. y(x) = y" + 6y'7y = 11e²x, y(0) = 1, y'(0) = 1 -7.x 11e2x 7e…

A:

Q: A survey was given asking whether people like dogs and/or cats. 123 said they like dogs 185 said…

A: Given that n(D)= number of people who like dogs=123 n(C)=number of people who like cats=185 n(D and…

Q: (1-3) (x+y) - 4 Find حرقیم CR لا لا للمعاد لك - 031- ans:- X 1

A: You posted multiple questions. As per our policies solving first question.

Q: 1. Let A = (a)nxn be symmetric and positive definite. Show that a) a>0, i=1,2,..., n. 1 b) |a₁|< (a,…

A:

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: Part (3) We have the statement "If the sun is a planet then 3 is even" Let p=sun is a planet Let q=3…

Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³; (4) y = x sinh 2x-cosh 2x (2) y =…

A:

Q: Prove that the 2nd smallest non-abelian simple group is of order 168.

A: Introduction- An abelian group, also known as a commutative group, is a group in abstract algebra…

Q: (3-zi) (x+y)=3+2i +ゾー

A:

Q: where do the curve of y = cosx and y=x²-1 intersect?

A: We have to find the point of intersection of the given equations. First we will sketch the graph of…

Q: 1. How many attended only the FSU-Butler game? 2. How many did not attend the Marist, Butler, or…

A: Given that total number of people are 445. To find: 1. Number of people attend only FSU-butler game.…

Q: (a) / Use the Shell Method to find the volume of the solid generated by revolving the region bounded…

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

Q: Let P2 be the vector space of all polynomials of degree ≤ 2 with coefficients in R, and S= {1 + 2x,…

A: The basis for the vector space P2 is 1, x, x2. We have to write the matrix form for the set S. We…

Q: Six college sorority sisters-Summer, Autumn, Wynter, June, April, and January-got together for their…

A:

Q: (a) If the graph is a polynomial, determine the minimum degree of the polynomial. (b) If the graph…

A: Please see the attachment

Q: 5. Use spectral decomposition to orthogonally diagonalize the matrix A = 5 10 {]. 5

A:

Q: Now compute the roots of the following equations: 1. f(x)=x²-cos(x) 2. f(x)=x-e* 3. f(x)=x²-12x³ +…

A: Note:- Equation (1) and (2) have trigonometric term so either we can solve this problem using…

Q: Simplify the following with out cesing + cеsingtue deного inator 5 3+i

A:

Q: The government gives 3 farmers each 200 yards of fence and tells the farmers that they can claim any…

A: The area(A) of a rectangle is calculated using the formula: A=l×w, where l is the length, w is the…

Q: Complete the following steps for the given function, interval, and value of n.. a. Sketch the graph…

A:

Q: (B): If A = 2t + 3j-4k; B=3i-4j+5k and C=i+j-k, find: (1)Ã.B (u)B.C (U)Ã. (B+C)and (A + B). (iv)…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Q5/ Find the area of the region in the first quadrant that is bounded above by y = √x and below by…

A:

Q: Which of the following vertices are adjacent. 7

A: If two vertices are connected by an edge, they are adjacent Check the given vertices 3 and 2 are…

Q: Every closed and bounded subset of X is compa The subset {z EX: |||| ≤ 1} of X is compact... X is…

A:

Q: Answer the following questions for the function defined on the interval [-5, 7]. a.) f(x) is concave…

A: From the above details we have,

Q: Find the general solution of the differential equation y" - 10y' +61y = 0. NOTE: Use c₁ and ce as…

A:

Q: со 2 + 1/5 1

A: Given as, y=cos2xx2+y2-x=2

Q: Let y = n=0 y' - 7y +11 x³ = 0, y(1)=4. Find 03. a3 03 = a3 None 269 3 268 3 271 3 a (x-1)" be the…

A: We have given a differential equation ,  y' - 7y + 11x3 = 0   with  y1 = 4 Let y = ∑n=0∞ anx-1n  be…

Q: Solve the heat equation u = 12u, 'XX' u(x,0)=(x-8). 8 ○ Au(x, t) = 2/7/7 | e-120²₁ sin[(x-8)]d w. 2A…

A: Introduction: The heat equation is a very important partial differential equation. The method of…

Q: Solve y" - 2y + y = 12e³t y(0) = -1 y'(0) = 0

A:

Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 8t = 0

A:

Q: Find b and c so that y = 8x² + bx + c has vertex (7,5). b C =

A: Here given that y=8x2+bx+c and has the vertex at the point (7,5) since the line of symmetry is the…

Q: Use the formula for instantaneous rate of change, approximating the limit by using smaller and…

A: Given:  f(x)=9xx

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.