Let 2E An and BE Sn show that Hhen Baß'E An.

Q: For A ∈ Mn(C) show that A = A1 + iA2 uniquely with A1 and A2 selfadjoint. Show that A is normal if…

A:

Q: 1. Let u, ER" prove that lũ ơi <ll||||||

A: we want to shoe that  u→·v→≤u→v→

Q: Given that en 2= V and en 3=W,express each of the fallowing in terms of vand w a) in zv0/3

A:

Q: Show that cl S = SU(Bd S) %3D

A: LetS⊆R, claim: closure(S)=S∪Bd S =S ∪ S' by definition bd(S) ={ x∈ℝ/x∉S° &amp; x∉(ℝ-S)°} let  x∈S∪S'…

Q: ands 1. Let m*(A) = 0. Prove that for every B, m" (BUA) = m" (B). %3D %3D

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

Q: If sup(S) exists, then it is unique ylgn ihi

A: The solution is given as

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

A: Given problem:-

Q: Let A = d e Assume that det (A) = -13, compute the following.

A: Properties of Determinants :If we given A , nxn matrix then i) The value of det(cA) = cn det(A)…

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

A:

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

A: Symmetric matrix

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

A:

Q: Prove az - ae that d az dz

A:

Q: メ (myst メート→ Q(2,4) where: Path C くz rom ○)と to over the Evaluate the

A:

Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

A:

Q: If E and E, are measurable , then (E,UE,) is not measurable. ylgn

A: False.

Q: Let j = 7 and U=span(ü), with ü = -6. Write j = ã1+ã2, where 1 in U and az in U-.

A:

Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

A:

Q: (- For all asb,C EZ,prove the folloNing (i)ala,1la, andal0; (ii)0la if and only if a=0; (iit)alb ond…

A:

Q: if it was Mzn (R) was =a,br Prove that MzmC to

A:

Q: dy If then de impossible to calculate O In(æ)

A: 7.  slope of tangent line  slope at point ( 4 ,2 )

Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: Suppose, X0- Binom(m,0)and 0~ Beta(a, B), then E(X) is equals to, a) maß b) aß ma c) d) me

A: Given: Suppose,  Xθ~Binom(m,θ) and θ~Beta(α,β)

Q: Let Sn=Vn. Find an and show that an O but that Sn=ER=1@k diverges. ->

A: Solution:-

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: 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: eb Let A E M₁ (TR) be given If AAt = On HOME JATOT prove that A = On - Does this hold if A EMn (C)?

A:

Q: Prove that for all values of the constant A, eAInt = e In.

A:

Q: Let A, B, and C e M,(C) such that ВС - СВ %3D А"А prove that BC = CB.

A:

Q: nd C such that AC=E

A:

Q: Let T={[a,0) : aER}, then T is not Borel algebra

A: Given a statement

Q: Given: HT || SF, LH = LS and HT SF Prove: AHOT ASTF

A:

Q: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

Q: Given: mAB = x Prove: mz1 = 180° - x A D Exercises 25, 26

A: Given:           m AB⏜ = x   To prove:              m&lt;1 = 1800 - x

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: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

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

Q: Show a Check for each. In othe 4) Find a. / (z + 4) dz

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Prove the following: %3D

A:

Q: In GL(2, Z,,). det

A:

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

A: Derivative.

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

A:

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

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

Q: (a) Prove that x, y = -1, y = 1 1 (b) Prove tha and n: m and

A: This is a problem of Number Theory.

Q: Show that Oa = {a} if and only if a e Z(G).

A: For a∈G, Oa denote the orbit of 'a' under the conjuction action.The orbits under the conjucation…

Q: If E and E, are measurable , then (E,UE) is not measurable

A: False.

Q: Consider the following coordinates. W(1,8), X (7,8), Y(4, 5), and Z(1,2) Select all methods you…

A: Given : W(1,8), X(7,8), Y(4,5) and Z(1,2) To find : All methods to prove triangle WYZ  is congruent…

Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B

Q: Hw/O Find Adi A if A. O kind Adj A il A=

A: (1). The given matrix is:  A=521  314  463