.If o + S CR is bounded above, then S has a supremum

Q: Given: LM = NO; LLMO = ZNOM Prove: ΔLΜΟ-ΔΝΟM M. N.

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Q: Find the value of k such that A is singular. 1 0 5 3 -1 0 2 k k =

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Q: Find the principal ideal (z) of Z such that each of the following sums as is equal to (z).   (4) +…

A: Known fact: m+n=d    where d=gcdm, n

Q: 9.G. Prove the Cantor Intersection Theorem by selecting a point xn from Fn and then applying the…

A: As per BARTLEBY GUIDELINES, I answered only one question (Q- 9.G) and                     repost…

Q: Use AAS to prove th Given: ZR and ZP a QR || SP

A: Given that, ∠R and ∠P are right angles. QR¯∥SP¯ We have to prove that, △QPS≅△SRQ

Q: Show that the following PDE is separable: tur + xu = 0

A: In this question, we solve the partial differential equation by separation of variable as…

Q: Given: - L KL ON OP NP Prove: ZM L = 2O * View

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Q: If D is an integral domain and if na = 0 for some a is non zero in D and some non zero integer n,…

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Q: Find a counterexample to Lie's Theorem when k is not algebraically closed and chark = 0. %3D

A: According to Lie's theorem, for any finite-dimensional linear representation of a finite-dimensional…

Q: Prove that L is solvable if and only if adL C gl(L) is solvable.

A: Please find the answer in the next step. None that a group is said to solvable if its derived series…

Q: Consider the set A = {1/2^{n-1}: n\epsilon \mathbb{N}}. Show that Inf(A) = 0. WITHOUT USING LIMITS

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Q: Prove that tr(aA + bB) = atr(A) + b tr(B) for any A, B belongs to Mn× n(F).

A: We need to prove that tr(a A + b B) = a tr(A) + b tr(B) for any A, B belongs to Mn×n(F).

Q: Which of the following is homogenous of smallest degree? (A) In x - In y B x+y x-y C √x-y x² + y4 X…

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Q: For wich of the following Lunchions is Roll's theovem applicabre in [o,2] O 2/3 f13) = (x-1) f(1) =…

A: By Rolles Theorem, for a function f:[a,b]→R, if  (a) f is continuous on [a,b](b) f is differentiable…

Q: Find the value of k such that A is singular. 1 0 3 4 -1 0 2 4 k k =

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Q: (a) Compute the following residue: Res 0 z°(1+2+ 22)*

A: (a) To Compute the residue Resz=0ezz5(1+z+z2)   Note: As multiple questions are asked, so only first…

Q: The Euler totient function is defined as ϕ (m) = |{k : 1 ≤ k ≤ m gcd(k, m) = 1}|,  or rather the…

A: Introduction: If p is a prime number and p|n, then ϕ(pn)=pϕ(n). Proof. You'll see that every number…

Q: Prove that if KCR is compact and non-empty, then sup(K) exists and sup(K) E F

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Q: find the poin ts of discontinuity of the following func tion s : (a) g (x,y) %3D (b) f laiy)

A: g(x,y) = 11-x2+y2The point of discontinuity is where g(x,y) approaches ∞. Or the denominator of RHS…

Q: For mighe. any integer exyelicsubysoup of osder Show tht /2 has

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: 3.19 Suppose if r = 0, f(x) = {-1)" if r E n+1' n where n E N. Prove: f € R[0, 1], even though f has…

A: Sol

Q: nd to wnwyun g ans 2

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Q: Show that the function f(z) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set f(r) = z and show…

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Q: A cubic spline S is defined by: So(x) = 3(x – 2) + (x – 2)² – 4(x – 2)ª 32 if 25x53 S(x) s,(+) =…

A: true

Q: c If in is an involution of X, show that (r, y)in = (yi", rin) is an involution of X12). %3D

A: Given X is a lattice. Given in  is an involution of X To show: x,yin=yin,xin is an involution of X2…

Q: If ø + SCR is bounded above, then .S has a supremum إختر واحداً: ibs

A: I have proved by contradiction

Q: - Prove thas the scries 2+x2 3+X2 4+x niformcy conuergen2 in any interval?

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Q: Which of the following is homogenous of smallest degree? A In x - In y x-y B /x-y x4+y* x+y

A: Let's find.

Q: Find the supremums of the following sets [1 :by proving your results .Si = {a < x < b; x E R} (a %3D…

A: Since, the question is of multiparts, according to the Bartleby Answering rule, only 1st questions…

Q: 1. Find the area inside the inner loop of r 3-8cos 0.

A: according to our guidelines we can answer only  first question and rest can be reposted.

Q: Let n E N coprime with p. Show that there exists x, y E Z coprime and such that p | x² + ny² is and…

A: To prove the given claim we have to show that :- x,y ∈ Z ; gcd(x,y)=1 ; p | x2 + ny2   implies…

Q: (b) There exists LE R such that L4 Size(O(n)).

A: Given below clear explanation

Q: If e denotes the unity element in an integral domain D, prove that me · ne = (mn)e for all т, п € Z

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

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Q: 1. Iff: [0, 1] R is defined as f(x) = x if x is rational, 1-x if x is irrational, discuss the…

A: Given :  f: [0, 1] →ℝ  is defined as     f(x) = x,if x is rational1-x,if x is irrational To find :…

Q: In the domain of Gaussian integers Z[i], the element 15 is 青 O Reducible O Unit O Irreducible O None…

A: Since 3∈ Z[i] and 5∈ Z[i] And 15 = 3 × 5 Hence 15 is reducible element in Z[i]

Q: If e denotes the unity element in an integral domain D, prove that me • ne = ( mn )e for all m, n ϵ…

A: We prove the identity as,

Q: For p = (1, 0) and x = (x₁,x2,...,xn) ER", define ||2|p:= - ². |P Show that n jyjx|py|q for x, y…

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Q: Suppose m, n ∈ Z + are relatively prime. The function f : Zmn → Zm × Zn defined by  f([Z]mn) =…

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Q: find the desivalive d the functian ha)= ainfse and compute h'(2) Th o

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Q: If m, n are relatively prime, then o(mn) = o(m)o(n)

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Q: 9) suppose that horx)=1, f,(x)=x ond dz(X) Prove that Ba(f, - where Ba is a Bernyterh Polymomial.

A: Given functions are f0(x)=1, f1(x)=x and f2(x)=x2 Since Bernstein polynomial is…

Q: 6. Let K be compact in R and let c E R. Prove that there exists a point a € K such that |c – a| =…

A: Given- Let K be compact in R and let c ∈ R.  To Prove- Prove that there exists a point a ∈ K such…

Q: - In the domain of Gaussian integers Z[i], the element 43 is O irreducible O reducible O unit

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Q: Let 5= [(a,0); VER] show that s is subring subring-ft

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Q: Let a > 1 be an integer. Prove that n|p(a" – 1), where o is the Euler ç-function.

A: In number theory, Euler's totient function counts the positive integers up to a given integer n that…

Q: Find the value of k such that A is singular. 1 0 6 4 -1 0 6 2 k

A: Given. A is a 3X3 matrix. We need to find the value of k for which the matrix is singular. Singular…

Q: Answer the following questions: 1] Find the supremums of the following sets by proving your results:…

A: We Know that  Suppose that A ⊂ R is a set of real numbers. If M ∈ R is an upper bound of A such that…

Q: Find the value(s) of k such that A is singular.

A: to find the value of k