with inner product product space Il x" =! Show that Let E be an inner Il Xx- x Il →0 nd ly, -yll->o then for each sequerce if くメ, y>→く lyn) in E. (Xn) and

Q: Lut a,bicid by integers such that ad-bc-1. For integes u and y, define Vi u's aut bv and ✓-cut du…

A: Let a,b,c and d be integers such as ad−bc=1. Let u and v be integers and define u'=au+bv and…

Q: E. If T:(x, y) -→ (x + 2, y), then T²:(x, y) → (_²_, _?_).

A: Given: Tx,y→x+2, y To determine: T2x,y→?,?

Q: what are domine, Vange and null space o F Tisra-s Ty Rom R?into Re 1

A: The given functions are                                 T1:ℝ2→ℝ2 such that T1ξ1,ξ2=ξ1,0.T2:ℝ2→ℝ2…

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

A:

Q: prove for all x,y in R^n: (1+||x+y||) ≥(1+||x||)/(1+||y||)

A: Sol:- The inequality to be proven is: (1 + ||x + y||) ≥ (1 + ||x||)/(1 + ||y||) Let's start by…

Q: ²*6²²y dy) dr 3

A:

Q: 3-) Find the pointls) to point Az(d,0) on x-3~y2 that are closest メ=2 25 +1,5 0.5 + - -ロ5 + 8.5 to…

A: here we have to find the point on the curve x=3-y2 that are closest to point A(1,0) let point is…

Q: a) Use Backward difference to find the Finite difference equation of the follow ди ди o'u -= C- xe…

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: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

A:

Q: show that L^1(R) a Banach algebra Commutative

A: We will define the multiplicative operation of Banach algebra in case of L1(R) and prove its…

Q: Shoe that Hhe p qiuen by norm on (on ho f be given by a scalar prodluct

A: We need to show that the norm on l∞ given by: x1,x2,…,xn,…∞=supxj: j=1,2,3,… can not be given by a…

Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

A:

Q: polation %3D

A:

Q: (L[u],v ) = ( Au, v)) = (Au)"C v = u"A"C v, (u,L*[v]) = (u, A* v) = u"MA* v. (9.5) Comparing these…

A: Given: Lu,v=Au,v=AuTCv=uTATCv u,L*v=u,A*v=uTMA*v   To prove: A*=M-1ATC

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: O Let ( X, T) be topdogical space and A,B CX- ldentify the Condition when a (Int(A)u FrlB) Ul F CA)…

A:

Q: Determine whether R is reflexive, irreflexive, asymmetric, antisymmetric, transi tiwe.

A:

Q: 子6)= cosz- Ga82-1., XE Co, 2T].

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Determine whether the function f(z)=z^2+(bar z) is analytical at z=1+i, where (bar z) denotes the…

A: Analytical functions, also known as holomorphic functions, are complex functions that are…

Q: Justify that (•, ·) defines an inner product on R?. the function (', ·) defined on R? as follows: U1…

A:

Q: Let A ∈ (R) be given If A is nonsingular, prove that adj(A) is nonsingular and adj(A)^-1 = (A^-1)

A:

Q: FX)= (x-4)²

A: Note: - “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: defermine whether is or divergent tonvergert Inin)

A: The above series is split into two as sum of two series as follows…

Q: for fuzzy sets A, B and C, (AVB)vc = AVIB VC). (Ал в) лс - АЛ(ВЛС). (A V BF = A“AR prove that AA CB…

A:

Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

A:

Q: Does the follorin relations hip define y as a real furction of x Why," AN

A:

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

A:

Q: 3. Prove the Distributive Laws: PV (q^r) = (pVq) ^ (pVr) and p^(qVr) = (p^q) v (p^r).

A:

Q: A³ f2 = V³ fs 3

A:

Q: Find the dircetiond Derevitive ef the Fouctiom 19(x2y)= Xye? at pl68, in the direchen oF Ol0,Og0)…

A:

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…