с) Let A :1, →1, be defined by Ах, х, ...) %3D (0, 0, х2, Хд, .). Prove that A is self-adjoint, positive. Also find VÄ.

Q: 3.) / sect 0 do

A: To evaluate ∫sec4θdθ

Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

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A: As per guidelines, we will solve first three subparts of the question. a) Given function is fx=-3x+4…

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A: Here, the objective is to prove the following: 1) 20+21+22+......+2n=2n+1-1   ; n≥02)…

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A:

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

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A:

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

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

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A:

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A: To solve the following problem and find F(3)

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A: We are given the equation ∂u∂t+a∂u∂x=c∂u2∂x2 , x∈ 0 , 1  , t≥0 Let us consider a grid of points in…

Q: əz Use Chain Rule to determine and where

A: We have to use chain rule step by step.

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A:

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

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A:

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A:

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A: The set T is defined as, T=a, b | a, b∈ℝ\ 0 The operation * is defined on T as follows, a, b*c,…

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A:

Q: Let T: R3 -&gt; R2 be defined by T(a, b, c) = (a + b, 2a —- c). DescribeT-1(1, 11).

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A:

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Q: which of the following statements is for t*t, the convolution oft with t" Select one: а. S. T(t –…

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Q: Q4. Let A E Rnxm, n ≥ m. a) Use the SVD of A to deduce the SVD of ATA. b) If m = n and A is…

A: Given: The given expression is, A∈ℝn×m , n≥m a) To use the SVD of A to deduce the SVD of ATA b) To…

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

A:

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Q: SELBCT ALL APPLICARLE CHC sin A) coverges B) diverges G. HI 20

A: We will use Ratio Test to check congervency

Q: dual of c, is isometric to l'.

A:

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Q: (1) Let F =x?++zÂ, and let u= ||FlI. Let fcu) = 3ue 2-2u Show thet Df(u)= 6-6u)eu F -2u

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Q: prove for n=l,2,3. e that +2+3+..+h = ncn+l) 2. %3D %3D

A:

Q: Q5:111M) A) Let f: [0,2]R be defined by (3 if xEQ if xeQ fx) = (2) feRn [0,2]. Show that (1) / is…

A: This question is related to limit and continuity .solve in step 2.

Q: Prove that the dual of l' is isometric to 10⁰.

A: Accounting to the given data, prove the given statement: