QUESTION 4 a) Let F(x, y, z)=x²7+(cos y sin z) + (sin y cos z)k be a vector space. Show that F is a conservative vector field. ii) Hence, find the potential function f, such that F=Vf. i)

Q: ILS] Demonstrate how any vector x ER can be expressed as a linear combination of the following…

A: Please find the answer of the first question in next step

Q: 10 8 -20 -18 -5 6 -9 -11 11 11 4 -5 -10 7 -9 1

A: Given A=-10-8-20-1814-56-7-9-9-111717111114-5-10   To Use: The Gram-Schmidt process to produce an…

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Q: 15. If x = t^2 -1 and y = t^4 - 2t^3, then, when t = 1, d^2y/dx^2= O 1/2 O 1/5 0 1 O 3

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Q: jw F(w). jw F(W) = jw F(W) = [ [2 - acos (WT) 2 - A Трия cos -2A (₁-COS (NT)) Тјия - 2A (asin ²…

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Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0).

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Q: 1. Consider the following subspaces of R³: U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R} (a)…

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Q: 33. Solve( L-¹. 3x+16 ²-5-6

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Q: 2² For the functions F₁ (ny) = 4 +2²+ng+g² and √₂₂ (m₂y) = n²³² +ng-n find the Hessian Matrixes H,…

A: Given functions are F1=x44+x2+x2y+y2 and F2=x3+xy-x Here ∂F1∂x=x3+2x+2xy=x(x2+2+2y)∂F1∂y=x2+2y For…

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Q: b. E=√CA-B

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Q: FT [f'lt) = jw flw) => jwF(W) = F(w) = JA -T T d+ + S (-A) 6² jut - just T ^ [e- jw+] = = = = […

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Q: jwF(W) = F(w) = T -jut Sqbote 4 Saps eibertat + -T A [eju+] = # [ @juy)] T -T -jw -jw AT Sim ² (WI)…

A: Assuming that the previous step is correct, we have

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Q: Don't change the W subspace. It is  W = {(x,-x, 2x): x, y ≤ R}

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Q: EX: Solve the ед. Ў+зу +2fy ht=zuct-)) , усо) =1

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Q: DO ) Find the interval of convergence where the power series Σ k=3 k² (3x −4)* - 2k+1 converges.

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