Prove that if n divides a, b, and c, then n³ divides a²(b – c) + b² (a – c) +²(b – a).

Q: Prove that: m3 = m – 3m,m, + 2m²

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 11. If QM = 6x - 11 and MR = 2x + 9, find MN. %3D

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: (c) 2, 3, 4+ V10 and 4. V10 are irreducible elements of R.

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Q: If m and n are integers and m x n = 0, then what is true for the values of m and n?

A: If m and n are integers and m×n=0

Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: In Z[V3], the element 2+v3 is:

A: Unit Given element is a unit

Q: inf a, + inf b, <inf(a, + bn), sup(an + bn) < sup a, + sup bn, n n

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Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 2. If BDbisects <ABCand m<ABD=10x-3 and m<DBC=2x+5, find m<ABC. A

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Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

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Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: Given constants a,b,c, and d such that  x2+ax+12 has factors of (x+4) and (x+b), and x2+cx-4 has…

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Q: Prove that AABC A DEF. C=2 E-4,2) 6-14.214 A 4) TF-.5)

A: Topic - transformation of a triangle Option 3 is correct Triangle ABC is translated by 8 units to…

Q: Apply any method to prove that if a|b and alc then a|(bc – 3c)

A: We will use direct proof method to prove the given statement

Q: need help with proof line alg

A: Consider the left hand side,

Q: Show that SU2(C) is simply connected and SO3(R) = RP³.

A: Consider SU2C group  SU2=α-β¯βα: α,β∈ℂ,α2+β2=1 To show it is simply connected we will show its…

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

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Q: Show that ∗ : R × R → R given by         (a, b) → a + 4b2 is a binary operation.

A: Given for all real number a and b

Q: Prove by contradiction that if m, n € Z, then m² - n is even or m-n-1 is even.

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Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

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Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

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Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

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Q: Prove, using an element-chasing argument, that {15n : n E Z} = {3n : n E Z}N{5n : n E Z}.

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Q: The Cholesky factorization of 53 is UTU where U is: 3 2 V5 5 -3 V5 1 3. 0 1/5] V5 5 3 0. 1

A: The given matrix is,5332

Q: If a and b are nonzero integers and m is the least common multiple of a and b, prove that (a) ∩ (b)…

A: Consider the given statement. (a) ∩ (b) = (m) Consider the left side of the equation. As, m is the…

Q: Σ Ea = n². %3D k=1

A: It is given that,  ∑k=1nak=n2

Q: Give a direct proof of the claim: V n E N, Vk E N, if the last k digits ofn are divisible by 2k then…

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Q: 3. Let A = {3k : k € Z} and B = {15m + 12n : m, n € Z}. Prove that A = B.

A: Let     A = {3k : k∈ℤ}    and          B = {15m+12n: m,n∈ℤ}To show :- A=B∵Let  x∈B  ⇒x = 15m1+12n1…

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

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Q: 471- 30. √2x-1=7 32. √6-2x = 4

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Q: Compute A B, where A AB= 0 -2 2 -2 0 2 -4 7 8 -5 -1 2 and B = 8 -2 1 -5 -1 3

A: This question can be solved using the concept of multiplication of matrices.

Q: If a is divisible by b, then bq, for some integer q. a

A: See the detailed solution below.

Q: 9-- 3 1 Prove that A abcd bcd a

A: The solution is given as

Q: Suppose b1 + *+ bm < n. Prove that b,!bm!< n!.

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Q: What is i in element a32?

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Q: Prove that √2 is not an element of Q(?).

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Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

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Q: If (ar + bx) = 4n and n+1 k-1 (ak - bx) = , then > ak = n+2 k-1 k-1

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Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: Show that: If |z| = 1, then: |z3 + 4z + 5 < 5 z + 5z + 6

A: Given: z=1 Then show that z3+4z+5z2+5z+6≤5

Q: Suppose a, b, and c are integers and suppose a b and ałc, where atc denotes that c is not divisible…

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Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: and (A) (B) = x, = 2x, = 3x, Show that if 8. N N (AB) _ (BC) _ (AC) 1 = y, then the value of neither…

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Q: Given that in the expansion of V1 + 2ax V1+ 3bx the coefficient of x is 2, and the coefficient of x²…

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Q: Q1: Prove that ; If CE AB, D E AB and C# D, then CD = 2 %3D

A: Key point: 1. There is only one line possible from two distinct points.2. The line is expressed in…

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: Show that yn Z, if n³+5 is odd then n is even

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Q: b If K = 4.1 x 10-6 then pK, Submit

A: This is a basic log problem