a finite dimensional normed linear space X, any subset M is compact if and only if M is closed and bounded.

Q: The sequence of eigenfunctions of a symmetric kernal can be made orthonoramal.

A: Suppose that, corresponding to a certain eigenvalue, there are m linearly independent…

Q: 7) Find the SVD of the following matrices: | 1 1 JF ii) 1 i) 1 1 1 2

A: The given matrices are: i) -111110  ii) -111112 We have to calculate the SDV of the given matrices.

Q: Find the sequence generated by the following exponential generating function: f(x) = e^x − e ^−2x +…

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Q: For the partial differential equation -882u dy² The PDE is (check all that apply) A. elliptic B.…

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Q: Stacey purchased a car for $58,300; she paid 5% of the cost as a down payment and financed the…

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Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

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Q: If (an) is a sequence converging to L, prove that (an)=1 converges to L.

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Q: A linear system is defined by three independent variables that obey the following equations 3x1 +…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Let (an) be a sequence and suppose that lim a2n = L = lim @2n+1. n→∞0 n→∞0 Prove that lim, an ² =

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Q: lim n→∞0 Use the ratio test to determine whether lim n→∞ diverges. (a) Find the ratio of successive…

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Q: Construct Green's function for the differential equation xy" + y = 0, 0<x<l under the condition that…

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Q: Solve the Laplace equation for the boundary Conditions and fly functions given below. ²T ax² + 3²7…

A: Using separation of variables

Q: Let f be a continuous functio to R. Let a and b be two distinct ntained in U and fbe differentiable…

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Q: 3. Define the function f(x) (a) Evaluate lim f(x) 1+0+ (b) Evaluate lim f(x) I-1 = 2x n+m m x YA m…

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Q: How To Solve It? Which Method? dy/dx-dx/dy= x/y- y/x

A: ∫(1/y) dy  =log y +c ∫ (1/x)dx = log x +c  ∫  ydy  =(y2)/2   +c  ∫ xdx   = (x2)/2   +c log(a)+log (b…

Q: If P is the projection on a closed linear subspace M of a Hilbert space H, then M is invariant under…

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Q: 5. Evaluate Fale JJJ (²+ + ² dv, where a, b, c > 0, and & is the region given by E 22 + y² 2² 6² +2…

A: Given triple integral is ∫∫∫Ex2a2+y2b2+z2c22dVa,b,c&gt;0x2a2+y2b2+z2c2≤1 in the first octant. Now,…

Q: For any collection a of subsets of X, there is ntaining a.

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Q: 00 x² So (1+x8)³ dx

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Q: For the following equation, Identify the conic, determine the standard equation, center, vertices,…

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Q: Consider the following IP. The optimal tableau for this IPs linear programming relaxation is also…

A: given max z=2x1-4x2s.t.2x1+x2≤5-4x1+4x2≤5x1, x2≥0; x1  ,x2 integer use the cutting plane algorithm…

Q: Cody borrowed $9100.00 from his credit union. He agreed to repay the loan by making equal monthly…

A: Solution:

Q: if I is an 18 an operador Hi them the following en апе 'a Hilbert space equila tent 1 T*T - I (1³)…

A: We know that , a Hilbert space is a vector space H with an inner product f , g such that norm…

Q: 9. Determine y at t=0.2 (0.2) 0.8 by the fourth order Runge-Kutta method, given that y' 1 t+y'…

A: To find- Determine y at t = 0.2 0.2 0.8 by the fourth order Runge-Kutta method, given that y' = 1t +…

Q: Let H be a Hilbert space, then a closed linear subspace Mof H reduces an operator T if and only if M…

A: To prove this theorm firstly we prove the theorm which states .. A closed linear subspace M of a…

Q: Determine wether. is B ~ S n=1 convergent 3 3 (√²+1 = ³√n²+1) 8W n = 2 the (2n-3)! (2n-2)! Series…

A: we have to find if the given series converge or diverge  1)∑n=1∞(n2+1-n3+13)2)∑n=2∞(2n-3)!(2n-2)!

Q: 9.12 Let f(x) be a function co each of intervals (a, c₁), (C₁, <bi.e. g(x) is a step functi- = f(a)…

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Q: n=1 BE n=2 2 n² = In (n) 1 In injen

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Q: Problem 2 (A) Show that y⚫T = Tv if and only if I is symmetric (B) Show that vx E = Exy where E is…

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Q: 1. Olivia takes a mortgage of BD 250,000 to purchase a house at a nominal annual interest rate of…

A: simple interest = (money×rate of interest×time)/100

Q: 4. Find a solution of the Bessel's equation of order zero.

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Q: Prove the locally compact normal linear space is finite dimensions.

A: We have to prove the  locally compact normal linear space is finite dimensions First we define the…

Q: Suppose we have a nxn linear system A = 6, but that the coefficient matrix A is not strictly…

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Q: Prepare (by hand) the final (simplified) equation system necessary to obtain the least squares…

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Q: Thong opened a compound interest account. He made an initial deposit of $1,078. The account pays him…

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Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 16 and the sphere x² + y²…

A: We have the solid that lies inside the cylinder x2+y2=16 and the sphere x2+y2+z2=36 Let x=r cosθ,…

Q: What is the prime factorization of 125

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Q: a) Find a, b if a + 2b = 116 mod 9 and 2a + b = -62 mod 7. b) Write the prime factorization of…

A: Note: We are allowed to solve one question/ three subparts at a time so kindly upload remaining…

Q: Function f then f) converges to fin measure.

A:

Q: 4) 9 fcx₁ = { * ** い x x 70 2r-19 x (R₂Tx) Let's see if I am (Topological continuity will be…

A: The given function is ; f(x) = x,x≥02x-1,x&lt;0 (a) Investigate whether the given function f : ℝ, T…

Q: 1. Find the area of the region bounded by the boundary conditions below: (complete with graph) a. y…

A: We have y=x+5 , y2=x , y=2, y=-1 Now, the region can be graphed as below: The area lies from y=-1…

Q: Q) Calculate the coordinates of the center of mass of the disc D bounded by the circle x² + y² = 2y,…

A: Given: The density of the disc is: fx,y=1+yThe disc D is bounded by the circle x2+y2=2y We have to…

Q: A company operates a fleet of delivery trucks. Study shows that gallons of fuel consumed per mile of…

A: Given Fx=k1x+k2x Differentiate w.r.t. x, F'x=-k1x2+k2F''x=2k1x3

Q: Set up the line integral ∫c x2z ds, where c is the line segment from (1, 6, -1) to (- 4, 1, 5). (No…

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Q: projection on a Hit bort space beat M and Mall space N, then MIN if and only if p is self-djoint and…

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Q: fixed a system of coordinates in the planes. Consider the having equation y = (x-2)². The line x=2…

A: The curve C is given by the equation                                    y=(x - 2)2  . . .  (1)…

Q: Let A5 = {5k|k € N}, A7 = {7k|k € N} Show that A5 A7 = 0

A: We prove our result by Contradiction method. First we suppose that our claim is Not true, then we…

Q: (8) Let A and B be m x n matrices. Prove that the rank of A + B is less than or equal to the rank of…

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Q: Define the map f: M2,2(R)→ M2,2(R) by f(X) FX-XF. You may assume without proof that the map f is…

A: Given :  F = 0010.  The map  f : M2,2ℝ→M2,2ℝ defined by  fX = FX-XF. To prove :  (i) f2X = ffX =…

Q: Brian purchased a car for $30,600; he paid 10% of the cost as a down payment and financed the…

A: Solution: