2. Determine the following sets: a) {r €R: (3n EN\{0}) 2n – 1 < nx < 7n - 2} b) {r ER: (Vn EN\{0}) 2n – 1< nx < 7n – 2}

Q: . Rewrite the equality of ideals (r+ y/2) = (3 – 4/2) in Z[/2] in terms of elements.

A: We know that, A subring  B of a ring R is called a ideal of R if for every r∈R and for every b∈B,…

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

A:

Q: 5**) (a) Prove that for all positive real numbers n, r, and s, if rs < n, then r < Vn or s < Vn.

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the next…

Q: 19 + 4x. Determine the zero(s) of q(x) = x

A: Recall: zero(s) of q(x) is set of all values of x in which q(x)=0 Given: q(x)=-19+4x

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: In the domain of Gaussian integers Z[i], the element 23 is * Irreducible Reducible Unit None of the…

A: (i) Every prime is irreducible in Z[i].

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: 2 2/The third term of a geometric sequace whose First term 2 and its FiFth tom 162 is ? A- az a 18…

A:

Q: Vhich among thế chôičes satist etters only. 2а. у" - Зу'- 10у %3D0 Co-5x C o2x

A:

Q: -145 2. find least 0అ కావులి Sంఖనాుంది spcave Axz b A z] 1 -4 1 1 2. 2. enter xas a Coloumn ve

A: Given that, AX=b A=1-4010012-1121,   b=3134 The least square solution to the system AX=b is the…

Q: Q3- Give an example of two denes not equal X subsets of (R,T) and (z, of ). ( Explain your answer ).…

A: Answere : The two example are given below :

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

A:

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: of Voots of the equation. 2x+3X+5=0 is The muttiple is Ę 2. 3 Prove That The sum

A: Use the formula for the sum and product of the roots of a quadratic equation.

Q: Show that \{e ^ (- x), x * e ^ (- x)\} is a fundamental set of solutions of y^ prime prime +2y^…

A:

Q: - such that n >r > 1, (n – 1)! r!(n – 1 – r) n! r!(n – r)! n - r -

A:

Q: (b) Show that 1+ 2/2 has infinite order in R*.

A: Given that R=m+n2 | m,n∈ℤ (b) The objective is to show that 1+22 has infinite order in ℝ×

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

A:

Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

A:

Q: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: 13 3. Use the IVT to prove that y = r Inr has at least one zero on 2 2

A: Above function is continuous function in given interval. So we can apply IVT

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: Use an inclusion-exclusion principle argument to determine the number non-negative integer solutions…

A:

Q: 3. Let n E Z. Give a direct proof that there exist x, y E Z such that n = 55x + 78y.

A: Objective : To prove for any n∈ℤ ∃x,y∈ℤ such that n=55x+78y Prove for n=1, Greatest common divisor…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: 13. Which of the following quartic fun tions has x =-1 and x =-3 as its only two real zeros? Oy=x-…

A: If -1 and -3 is zero of function then at -1 and -3 value of function must be 0

Q: 4. Prove C(n, r) = C(n- 1,r- 1) +C(n- 1, r) %3D using a combinatorial proof.

A: We know, C(n,r) = n!/((n-r)!r!)

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

A:

Q: 4. Let R be the set of all real numbers, xER and n EN such that n > 2. If (1+x) >0, prove that Pn :…

A: Mathematical induction.

Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

A:

Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

Q: Compute the convolution x[n]*h[n] for all n> 0, by using Graphical or Tabular method. x[0] = 3, x[1]…

A:

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0.

A:

Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: Prove or disprove: If xn ≥ 0 for all n ∈ N and lim sup xn = 0, then xn → 0

A:

Q: 2. Suppose that {v1,... , Vp} is an orthonormal set in R", and that x E R". What can you say about…

A:

Q: Oct 31, 2021, 16:44 Problem-2 0 Let foo = x?-2a and gcauz VI-x 6) is q CG (-Z)) defined! domain ind…

A:

Q: True or False? If d = gcd(a,b), then there exists integers x, y such that d = ax +by

A: solution.

Q: 4.By applying the Convolution Theorem to calculate L-1 is obtained: Determine the value of (a+b): a…

A: We have to find the solution.

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

A:

Q: By expanding both sides of the identity (1+ x)"+4 = (1+x)"(1+x)* prove that ("**) - (") + «(,",) +…

A:

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

A:

Q: Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1,…

A: Here we have ∑n=0∞(-1)nxnn6n=∑n=0∞an ⇒an=(-1)nxnn6n

Q: Which of the following conditions is sufficient to guarantee that integers x, y, and z satisfy the…

A: x(x-y)+y(y-z)+z(z-x)=1 Put all the given conditions and check which one is valid.