Prove (t, to) = A(t)Þ(t, t,)

Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

A: It is given that

Q: Let X N(u, 1) of size n. Obtain UMVUE for u.

A: Given that  Let X  N(μ,1) of size n. Obtain UMVUE for μ

Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

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Q: || Evaluate the follo dt t In(t) Note: Don't forge

A: Given: I=∫dttlnt    ....(1) Let, u=lnt Now differentiate on both sides with respect to t.…

Q: Prove Theorem (A + B )T = AT + B T

A: Prove Theorem (A + B )T = AT + B T

Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…

A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at

Q: If --kr, show that d? dr %3D dt

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: Let r(t) = (t, 3 cos(t), 3sin(t))

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Q: et T E L(V,W), and U e L(W, X). Prove that UT : V → X is also linear

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Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: alue of the pur C: |z| = (:-1)(z-

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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: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: y Verify Euler's theorem for u = x' In

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Q: find the values of c that satisfy Rolle's Theorem

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Q: is R* is contractible?

A: This is a problem of Topology.

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: what will be the valid conclusion for the given hypothesis: "f U is the midpoint of HT Then HU TU…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Let r, y EN such that y # 0, then y+r#0.

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Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: How to solve this?

A: We are given that x + y + z = 5 where x, y, z ∈ R. Now, we need to prove that x2 + y2 + z2 ≥ 5/3.…

Q: prove that T= S.

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Q: Let f(z, y, z) = z2 +y? + z²,z = /utv, y = /u – v, and z= uv, Find in terms of u and v.

A: we have to partial derivative with respect to u by using chain rule

Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

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Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: Define T:R → R' by T(x, y, z) = (x-5y+4z, y- 6z). a) Is T one-to-one? Justify your answer. b) Is T…

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

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Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: Compute t a t2 ctan(t)dt. Hint: Note that 1- 1+ t2 (21)- 1+ t2 ftarctan()dt +C %3D

A: The given integral is ∫t tan-1(t) dt

Q: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

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Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

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Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: Let fun chan defined by g(2) = V Z+8' –-8, ts devivalie z+h+8- Vz+ 8 is equal to the expressian. A)…

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Q: Prove that (A+B)T=AT+BT

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Q: on vectors for t2 0.

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Q: Let fons =loag, Cln). Find t'ot at

A: Given, f(x)=logx(ln(x))

Q: s defined over ai at one point in tl асcordi

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Q: Prove that S, pm (x)Pn(x)dx = 0 if m# n ? %3D

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Q: Evaluate t* In t dt

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Q: Show that (A − B)T = AT − BT .

A: We have to use the properties of subtraction of matrices and matrix transpose operation. In matrix…