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

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: Given: WZ 1 bis. XY Prove: AWXY is isosceles. (Hint: This proof can be written in three steps by…

A: 2. given  WZ↔ ⊥bis XY¯ as WZ is bisector of XY XZ=ZY......(1)

Q: Find the alue of C that satisfied the theorem for the function fCx) = 3+ Jc on the %3D in terval…

A:

Q: Howin If Z=RCxy) and u=xayg V=x-y show that 3

A:

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

A:

Q: Prove Theorem 8.2.3 for the case where O lies in the interior of ZAPQ.

A: According to the given information, it is required to prove the given theorem for the case 0 lies in…

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f + 3g, v= fg, find the Wronskian of u…

A: It is provided that the Wronskian of f and g is tcost-sint. We need to determine the Wronskian of u,…

Q: Let xe c and ye show that <xiy= y AX is qu inmer product if A is hermition positive del iniite

A: (Solving the only one question as per our guidelines) Question: Let x∈ℂm and y∈ℂm Show that x,y=y*Ax…

Q: If la,} and {b„} are divergent then {a, + b,} is divergent. True False

A: Given: an and bn are divergent . The objective is to state whether an+bn is divergent is true or…

Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: 1. Identify which theorem will prove that ZEDC = ZDEC= ZECD if DE EC = CD. A,

A: Given problem:-

Q: XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove that…

A: The answer is given as follows :

Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: 25 If A E M, is symmetric, prove that AT is symmetric.

A: Symmetric matrix

Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

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

Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: Drag the postulate or theorem that proves the trieng AZWX AY XW a. ATSU AXVW # SSS E SAS

A: which criteria follow to congruent triangle

Q: if JERLA.b] and it hex)- J(x). except for finite mumber of Paint in Cab] then that he Rlab] prove.…

A: if g ∈R[a,b] and if h(x) = g(x) except for a finite number of points in [a,b] then prove that h…

Q: Let xe" and yer show that <xiy)=ytx is on imer product %3D

A: We have to show that &lt;x,y&gt; = y*x is an inner product

Q: 4. Show that the norm on (° given by I| (21, ..., In...) |lo= sup{|7;| : j =1,2, ...} %3D can not be…

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Q: Let A, Be Mnxn (F). (a) Prove that if A~ B, then At ~ Bt.

A: From the given information. The matrices A and B belong to M of order nxn. It is required to prove .

Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: If the i, j entry of A is i times j, show that det A = 0. (Exception when A = [ 1 ] .)

A:

Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: Show that every positive sol fron of Ay + B, k=osl,2- & bosunded, %3D JK is i-e, ogy sB-if A<1. 1-A

A: Given yk+1=Ayk+B, k=0,1,2,... Then the objective is to find the solution at which the sequence is…

Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

A:

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

A:

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

A:

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: Show that the functions x and x2 are orthogonal in P5 with inner product defined by (5), where xi =…

A:

Q: show that the. following Complex functron is dis continuous at z=i. fCZ) = スー! %3D 3.

A:

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: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: Suppose f" exists and is bounded on Co,0), Prove that if bam fa)=0, then bim fGx)=0.

A:

Q: 1. Obtain the weak formulation for the following BVP: in Ω, -V (kVu) = f u =g on ô0.

A:

Q: Prove (x + y) + z = (x + z) + y without using induction.

A: It can be solve using group theory

Q: 2) Suppose S,T E L(V) are such that ST = TS. Prove that null S is invariant under T.

A:

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

A: Given, We want to prove that

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

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

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

A:

Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A: