0 then Prove: If a, b, c, a, and M are constants and M 2 су — Мx* ах*у" + bxy 0 ba c constant) if and only if aa (a - 1) = Ax" (A Ур has a particular solution

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: Prove that Σ (2n+1) P(x) no (1-2hx+h²) ¾/2₂

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Q: 2. Use the inclusion-exclusion principle to find the number of solutions to the equation r+y+: = 19,…

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Q: 9. Suppose g(u) = | V1+t³dt. Find the value of (g¬1)'(0) if it exists. If it does not exist, explain…

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Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

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Q: find An eignuector of the matix 12 17 2 VZ V3 19 2 J3 -VIT -2 Ji

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Q: (a) Show that xn → x and Yn →y implies Xn + Yn → x + y and also show that an -→ a and Xn → ax. → x…

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Q: Q5: prove 1) e2-j3n-e² = 2) |e²| = ex

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Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: 2 1-X ie 2=tny then prove that da

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Q: 5. If Z1 = V3 - 2i, Z2 = -i+1 and Z - 3= 4i – 2. Evaluate (i) Re{3Z -5Z +2Z}} (ii) |(1+ Z, + Z3)(i –…

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Q: 17. Find a, b, c in Q such that (1+ V4)\(2 – V2) = a + bV2 +cV4 Note that such a, b, c exist, since…

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Q: Example Solve z"+ 512U3+ j512=0 or Find all the roots of fl3)=2"+572V3+j5]2. 10 on What ure the ten…

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Q: 10- Solve the problem: Utt-4uxx = xt, 00 u(x,0) = x, 4(x,0) = 0, u(0, t) = 0, Ux(1,t) = 1+t, t20 %3D

A: Given, utt-4uxx=xt;   0<x<1, t>0 ⋯⋯⋯⋯1ux,0=x,   utx,0=0,   0≤x≤1,⋯⋯2u0,t=0,   ux1,t=1+t,…

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: Q1(i) Prove that 1 1 1 + 2n²+1 V2n2+2 V2n2+n]

A: To prove: lim 12n2+1+12n2+2+.........+12n2+n=12

Q: Show that ri =1+i, r2 = 1-i is a solution of (3+ i)x + (1+ i)x2 = 4 +4i %3D

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Q: Prove or give an counterexample to the statement that for any neZ+ and aeZn, the equation +n X = a…

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Q: Let A = 2 2 1 24 2 0 23, 1. Compute L such that A = LU, where U 2. Solve At = 6, where L-¹6 = () 0 =…

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Q: 2. Solve the following Cauchy problem: u = u -0 0, u(x, 0) = 1 -1, u(1,0) = 4r, -00 <I< 00.

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Q: 8 (2-15)*- 3-V5 (a) Express in the form p + q5, where p and q are integers. (b) Given that = ab°,…

A: To solve the given problem we use the following result (a - b)2 = a2 + 2ab + b2 , (a+b)(a-b) = a2 -…

Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: 1×2° +2x3° +...+ux («+1)' _ 3u + 5 1° x2+2° x 3 +...+u² ×(« +1) 3n +1 +u X Зи + 5 Show that

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Q: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

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Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: Show that if x ~ Nm (u, 2), where N is positive definite, then (x – u)'N-I (x – µ) ~ Xm: 2

A: Given  x~Nmμ,Ω, where Ω is positive definite.

Q: 5 Suppose Te L(V), m is a positive integer, and v eV is such that T-v0 but Tv=0. Prove that v, Tv,…

A: According to the given information, Suppose that:

Q: If X ∼ N (μX , σ2X ) and Y ∼ N (μY , σ2Y ) are independent, then prove X + Y ∼ N (μX + μY , σ2X +…

A: X~Nμx,σx2 and Y~Nμy,σy2 are independent. Here, X~Nμx,σx2. In this context, it is known that the…

Q: 8. How many integer solutions are there to the inequality Y1 + y2 + Y3+ y4 0, 0 < y2 ≤ 10, 0≤ Y3 ≤…

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Q: Q3: If you replaced the coefficients of x1, x2, and x3 by 50, 20, 10 What is your final JJI Jguz lio…

A: Here, We have to replace the coefficient of x1, x2, x3 by 50,20,10 Than we have to answer the…

Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

A:

Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

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

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: (2 Let xinN(0.1), n = 2 and T= Xx +X2 Show that Tis a Sufficiency Stakistic.

A:

Q: I need help doing number 7

A: We start solving the given equations simultaneously.

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

Q: 341 Show that the Neumann problem v'u = 1 in r+ y' < 1 du - 2 an on x² + y' = 1 does not have a…

A: We will use greens theorem

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

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Q: (a) Show that any finite linear combination of the solution of following n th -order difference…

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Q: Show that o () –1 is an implicit solution to 2 -2y on the interval (-00, 00). Inload our

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Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: Both Newton and Leibniz were satisfied that their calculus provided answers that agreed with what…

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Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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Q: True or False 1. If Cov(X, Y) = 0, then X and Y are independent 2. If X and Y are independent, then…

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Q: If X ∼ N (μX , σ2X) and Y ∼ N (μY , σ2Y ) are independent, then prove

A: X~Nμx,σ2x and Y~Nμy,σ2y are independant

Q: 9. Solve the following Neumann problem: Uzz + Uyy = 0, 0<x< 2, 0 < y < 1, Uy(r, 0) = u„(x, 1) = 0,…

A: Given a Neumann problem.

Q: If both z + w and zw are real, how to prove that either z = w (conjugate) or Im(z) = Im(w) = 0?

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Q: Prove that JI = J [1 0 0] I = |0 1 0 Lo 0 -1 2 -31 J = 4 5 -6 %3D –7 8 -9 1.

A: Considering the matrix multiplication of J and I

Q: 3) Calculate: AВ-ВА , АС-СА , ВС-СВ Where 1 1 0 1 A 1 1 B -1 1 0 0 V2 Vzi 1 0. 0 -1 0. -1

A: I have found each product term one by one