Let AB = AC. Prove that if det(A) = 0, then B = C.

Q: 18) (SAnn B anlogbro dtiv C AB = 12, BC = 3x + 6, and AC = 5x – 12 a) Find BC b) Find AC

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

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Q: Is A – (B U C)= (A – B) N (A – C)? Prove it or disprove it.

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

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Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

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Q: Prove that I(e) = dr, e> 0.

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

A: The solution is given as

Q: GA Given: AC FB TO BC Prove: AB GF

A: Given : GAAC=FBBC To prove : AB¯ ∥GF¯ Proof : If possible let AB is not parallel to GF. So let us…

Q: Let r = xi + yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Prove that the following relationship is true: nCr + nCr + 1 = n + 1Cr + 1

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Q: Given: AB = Dc and AC = DB. Prove: AABCE ADCB. A B C AB DC gven AC DB g ven BC CB A ABC ADCB…

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Q: Let m eN and a E Z be such that (a, m) = 1. Let i, j e N. Prove that if om(a) = ij, then om(a') = j.

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Q: Show that For all z E C, with z # 0, then: |z/²z=1 = z

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

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Q: Given that w = f (u, v) And u = xz. , V = dw = X az aw aw Prove that Z - ду

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

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Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

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Q: Given: AB | DC, AB = DC Prove: AABD E ACBD

A: Given : AB∥DCAB≅DC

Q: If f = xi+ yj+ zk,1Fl =r,and n =, then show that grad (E) == %3D

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Q: Let a, b, c E Z. Prove that if a b and alc, then Vk EZ we have a (b+ ck).

A: ab  &amp;  ac   Since ab, therefore b=a·m   ,  where m∈ℤ Since ac, therefore b=a·n   ,  where n∈ℤ

Q: Let c E R and suppose that an → a. Show that can → ca.

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: Prove that (aA + bB)t = aAt + bB t  for any A, B belongs to Mm× n(F) and any a, b belongs to F.

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

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

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Q: nd C such that AC=E

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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: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

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

A: Given a statement

Q: Prove: Provided it exists, (A-1)¯ = A.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: ), P{|Zn – c| > ɛ} → 0 as n → o. Show that for any b on g, E[g(Z„)] → g(c) as n→o

A: *Answer:

Q: If z, w E C, prove that z+w=z+w.

A: This follows from simple substitution. The detailed solution is presented in step 2. As requested i…

Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: Prove: (i) b (A) CA if and only if A is closed. (ii) b(A) n A 9 if and only if A is open. (li1) b(A)…

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Q: of af 42. Assume that w = (х, у) — ху, and (х, у) ду dw dw Find and at ds

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Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: Let T={(a, 0): aER}, then T is Borel algebra.

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Q: Given: CE= FH CD GH G. Prove: DE = FG

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Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x&gt;0, r&gt;0, λ&gt;0 Y~Gammas,λ fy=λsΓse-λyys-1,     y&gt;0,…

Q: Prove that if X₁X and Ync, then (Xn, Yn) (X, c).

A: For a sequence of random variables X1, X2, X3,... to converge to a random variable X, we must have…

Q: if w= /x2 + y2 + z2, x= erCos0, y=erSin0, z=ee prove that aw/ar= e?r/w and aw/ae = e20/w

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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: Let A E Mn(R) be given. (a) If det (A) = 1, prove that adj (adj(A)) = A. (b) If A is nonsingular,…

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: Let A EMn (R) be given. If 11x11 = 11yll = 1 and x •y = 1, show that x=y

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Q: By using Caushy Rieman prove that (2) and (3) (2) 4ca) = e (3) .w prove Thot()-

A: (a)

Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

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