Assume that a1, a2, ..., an E R (with n > 2) such that a1+a2++an = 1. Prove that af+az++a > 1 (Use Cauchy-Schwarz). n

Q: by computing that the given funetions inde pendent on Show the are linearly indieated intorvale…

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Q: Prove that det(kA) = kn det(A) for any A ϵ Mnxn(F ).

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Q: By using caushy Rieman prove that C. Prove thatd az az ae

A: According to the given information, it is required to use Cauchy Riemann to prove that:

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Q: Prove that (C, +) ≈ (R × R, +).

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Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

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Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: 1. Prove by Induction that the numbr f edges of Kn

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Q: Compute the orthaganal piojectian of ? onto the lina L through -6 and the origin

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Q: Evaluate the following iterated integral. -7cose 5 rdrde 49 n+ 5sin 40 49 2n+ 5sin 7 2 n+ 5sin 40 49…

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Q: Prove that the set S = {n² : n e N} is denumerable. %3D

A: We have to show that the given set S is a denumerable set.

Q: Prove that c(u × v) = cu × v = u × cv.

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Q: Show that A is symmetric if and only if ai j = aji for all i, j.

A: We know that a matrix A is said to be symmetric if and only if A^T = A; where A^T is the transpose…

Q: 1. Prove that the followingn is a theorem in SD. Av - A

A: Theorem :-

Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

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Q: Prove that on average, permutations of length n have H, cycles, where Hn i=1

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Q: Show that there exist m and k such that ma + kn = 1if gcd(a, n) = 1

A: Let gcda,n=1.

Q: Show that A is skew symmetric if and only if ai j = −aji for all i, j.

A: Suppose A be any square matrix of order n such that A=a11a12⋯⋯a1na21a22⋯⋯a2n⋯⋯⋯⋯⋯an1an2⋯⋯ann First,…

Q: 1/3 If (x+iy) =a+ ib, Prove that

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Q: Prove that ||A||1 = max1<j<n{£", |aij|}. %3D

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Q: Prove that u + v and u - v are orthogonal in Rn if and only if llull = llvll.

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Q: 1 Show that n2 + 1 IN V

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Q: Let a and b be any real numbers. Prove that Cov (ax, by) = abCov (x, y).

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Q: Prove that on average, permutations of length n have H, cycles, where Σ Hn i=1

A: We will take an arbitrary set containing n elements and observe the required permutations.

Q: Prove that, IXI<a Rf and If -aL X Z a

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Q: = Prove that E = ehd.

A: We know that Ef(x)=f(x+h)

Q: 3.) Prove that P, is a all ve ctor by showing space 10 0xioms ore

A: proof P2=a0+a1x+a2x2:a0,a1,a2∈R   is vector space over + and ×first we proof P2 is abelian group…

Q: Let us assume the facts for all a, 6 E R, i.e. as < bi whenever a < b. Let SCR be bounded above and…

A: Given that S~=x∈ℝ|x3∈S And S⊂ℝ is bounded above. We say that S⊂ℝ is bounded above if  and if…

Q: Prove that Qis dense in R

A: We prove that Q is dense in R.

Q: prove that 2,

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Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

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Q: Prove that the Kronecker delta and Levi Civita symbols are tensor of rank 2 and 3, respectively.

A: Prove that the Kronecker delta and Levi Civita symbols are tensor ofrank 2 and 3, respectively.

Q: The random walk in one dimension is certain recurrent. at, for large n, u2n N de a proof, courtesy…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Give en exem ple of e: neer trensforme tion thet is not invertibl. V-> v onto but

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Q: Let A be an wmxn matcix Prove that %3D

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Q: Determine all the number(s) c which satisfy the conclusion of Rolles Theorem for

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Q: prove that tr(aA+bB)=atr(A)+btr(B)for any A,B belongs to Mmxn(F)

A: Let A=aij and traceA=trA=∑i=1maii.. Note that, aA+bB=aaij+bbij. Then,…

Q: 5. Prove by taking z = a + bi, z – z = 2iIm z.

A: 5) The given complex number is z=a+bi. Here, Rez=a and Imz=b. For any complex number a + bi the…

Q: Prove that (i) Res (tan z, r/2) = - 1

A: Here,we have to prove that Res(tanz,pi/2)=-1

Q: By using Cauchy Residle Theorem 到一2p 121=1

A: First we have to find residue at singular points.

Q: 5. If u = ee Cos(alogr) prove that a'u 1(ôu 1 a'u = 0 + r ôr

A: Derivative.

Q: Use the glven informatlon to prove that ARST AVUT. V Given: RT e VT ZRST ZVUT U S. Prove: A RST AVUT

A: in the given ∆RST and ∆VUTGivenRT≅VT∠RST≅∠VUTTo prove that ∆RST ≅ ∆VUT

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: Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3D

A: Given, We want to prove that

Q: Let T be. a linear trans formadion

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Q: Which theorem can be used to prove that ΔROM ΔΡΜΟ M P.

A: We can answer the question as below

Q: Prove that det(kA) = kn det(A) for any A ∈ Mn×n(F).

A: In determinant the scalar quantity is taken common from a single row or a column.