4.33. (a) Evaluate f (x+2y) dx + (y-2x) dy around the ellipse C defined by x = 4 cos 0, y = 3 sin 0, 0≤ 0 < 2TT if C is described in a counterclockwise direction. (b) What is the answer to (a) if C is described in a clockwise direction?

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A: We have to prove that   22×5+52×8+82×11+········+3n-123n+2=14n(3n-1)(3n+2)(3n+5) By using…

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Q: 16. (a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x || for every vector x ER" where…

A: Given: (a)Q is an orthogonal matrix.          : (b) Qx=x To Prove: (a) Qx=x               : Q is an…

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Q: Solve the following linear system by Gauss elimination. If the system is inconsisitent, type "NA" in…

A: Given system of linear equations:-2b+8c=103a+12b-9c=-99a+34b-19c=-16

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Q: Let 0 0 -1 Obtain a basis for each of the following subspaces: -1 (a) N(A). (b) R(A). -1

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Q: A Moving to another question will save this response. Question 10 (3x-y+42y+z-x,x+y+z) relative to…

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Q: Proposition 4.1.3. Let A CRn be open. Iff: AR" is C¹, then f is locally Lipschitz.

A: Given: A function f:A→ℝm which is C1, and A⊆ℝn is open. To Prove:  f:A→ℝm  is locally Lipschitz.

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Q: The third column of the change of basis matrix from the basis B= {u=(1,1,1) ; v= (1,0,1); w=(0,1,1 }…

A: Given two bases are  B={u=(1,1,1); v=(1,0,1); w=(0,1,1)}   and  B'={r=(3,4,1) ; s=(3,0,1) ;…

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Q: Let A = 1 and let b = 3 0 1 (a) Use the Gram-Schmidt process to find an orthonormal basis for the…

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Q: л There

A: We prove our result by using definition of mod.

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Q: Proposition 4.1.2. If ƒ : A → Rn satisfies the lower-Lipschitz condition on E, i.e., if there exists…

A: We will prove all by using the definitions

Q: Eliminate the parameter and describe the shape of the curve: :=√√x+4; _y=3√t; for 0≤t≤16

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Q: Hey please fix this. I can't see the solution.

A: Given: The matrix B is given by:     B=100100-2520 To Find: We have to find: (a) The eigenvalues of…

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Q: Express the vector = [4] à = vi+ as a a linear combination of ₁ = [] [1] and = [] 02 V2-

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Q: a. The first seven terms of the Fibonacci-like sequence with seeds 0, 4 F₁ F2 F3 F4 F5 F6 F7 ...

A: Fibonacci sequence, in which each number is the sum of the two preceding ones.  Here, it's given…