Problem 5 Let (X, M) be a measurable space. Prove that the linear combination for µ= >ak Hk. k=1 ak>0 miaru, ...µ, defined on the o -algebra Mis the measure on M.

Q: (a, o) is not measurable.

A: to find that a,∞ is measurable or not  proceed as follows We know that every interval is measurable.…

Q: 5. Compute F-dà where F= zk and Sis the rectangular plate with corners (0, 0, 0), (1, 0, 0), (0, 1,…

A: To find -   Concept used -

Q: Ex: © Suppise that the fiowing Aransferuntin Conneclğs the lei) and (ti) coordnate Syshems; a4ス?) 2…

A: Given that, ζ=x¯1=ex1+x2x¯2=ex1-x2 To find: a) Jacobian matrix J and J-1 b) Compute J¯

Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: 1. (J · K) v (~ J. ~ K) / :. J = K

A: There are three expression in the given logical statement. They are J.K ~J.~K J≡K We prove the two…

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 8. Theorem . mCF 41 53

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Q: 4y² Given the function f(x,y)= find each of the following. SIMPLIFY A) f,(x,y)=. B) f,(x, y) =- C)…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

A: Here is how the set S is defined: S = {(a, b, c) | a, b, c ∈ [100], a &lt; b, a &lt; c}   We must…

Q: Given that w = f (u, v) And u = xz. , V = dw = X az aw aw Prove that Z - ду

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Q: Calculate the minimum value of 9x + 6y subject to the following contraints: x + y > 22 x + 2y > 27…

A: we solve this LLP by  graphical methods.

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Suppose thet the filowing Aransforuution Conneclss the (x') and (ti) codmate ک ماول se4ス?) e え(スーx)…

A: Handwriting solution given.

Q: Given A = A(x, y) subject to bzx+ byy <B and Cxx+ Cyy <C i) Write the Lagrangian function. ii) Write…

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Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: (d) Derive expressions for the variance of Bi and the variance of the least squares estimate 3…

A: Given,     The simple linear model is given by                yi=β0+β1xi+ei, i=1,....,n   and…

Q: (1,0) C is the path from (1, v2) to (1, 0) along line segments as shown in the figure above. Then…

A: The application of line integral is, it represents the work done by a vector function acting along a…

Q: Name the preimage of R'. T' T V' R' R Your answer: O T O V O R

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Q: what is the averaage value of y=a/x on [1,b]?

A: First we have to find formula of average value.

Q: Suppose SR" is convex. Show that cl(S) is also convex.

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Q: Let f(x, y, z) = x³ – yz?. Find af af of and ax' dy az

A: Given : fx,y,z = x3-yz2

Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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Q: For each of the following sequences, if the divergence test applies, either state that lim an does…

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Q: If F(x, y, z) = (sin x + 2) i+2xz j+ (e-x) k and the path C is the line segment from A(1,2, 1) to…

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Q: ndwritten please Rew

A: Introduction: A Boundary price drawback may be a system of normal differential equations with…

Q: " 4 Let y = 8 1 W = Span {u₁, U₂}. a. Let U = [u₁ u₂]. Compute UTU and UUT. b. Compute projw y and…

A: Given: It is given that y=481,  u1=2/31/32/3,  u2=-2/32/31/3, and W=Span u1, u2. Consider, U=u1, u2.…

Q: Prove z = max (x,y) and z = min(x,y) are convex

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Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

Q: Z = In z + X + find the det ermain Z as Function given equation adiff erential X änd

A: