1. List a pair of zero divisors of (M₂(Z), +, ×):

Q: 3. Given the polynomials p1 = t3 – 2t2 + 1, p2 = t2 – 4, p3 = t3 + 2t, p4 = 5t. Does this set of…

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Q: 5. x₁ + x₂ -3x1 3 +2x30 X₂ - 2x3 = 2

A: According to Bartley guidelines, these are separate questions. Please ask second question…

Q: Q1-Using the nodes (x, =2, x-=2.5 and x; =4), to find the second interpolation polynomial for flx) =

A: Given nodes are x0=2, x1=2.5, x2=4 and function is f(x)=1x Now table is x 2 2.5 4 f(x) 0.5 0.4…

Q: Determine integers x and y such that (а) gcd(51, 288) — 51х + 288у (b) gcd(357, 629) = 357x + 629y

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Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: 2. Given the points (1,0.7),(2,0.73),(3,0.8),(4,0.75),(5,0.6). Use Lagrange polynomials to find the…

A: Given points are xi 1 2 3 4 5 yi 0.7 0.73 0.8 0.75 0.6 Here, i=0, 1, 2, 3, 4.

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

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Q: Show that the multiplicity of (x-1) is 1.

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Q: If β is a zero of x2 +x + 2 over Z5, find the other zero.

A: Given: The expression x2+x+2 over  Z5 has β as zero. To find: The other zero of the given…

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

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Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

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Q: In real analysis,Prove that if A is countable, then m(A) =0.

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Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: Multiply: 3y2(2y³ - 4y² + 5y) a. 6y5-12y + 15y³ d. 5y5-y¹ + 8y³ b. 5y6-y4+8y² e. 6y5-y4+ 15y³ c. 6y6…

A: SOLUTION-

Q: Solving O.D.Es: Use the method of separation of variables to solve each differential equation. If…

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Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: 4. Factor a? + 12ab + 32b2. OA. (a+4b)(a + 8b) О в. (а - 4b)(а - 8b) С. (а - 4b)(а + 85) D. (a +…

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Q: Give all of the zeros of P(x)=x^2+4 as a comma separated list.

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Q: Indicate the least integer n for which (3x6 + 2x2)(x3 + 3x) is O(xn).

A: Solution:-

Q: Prove that (p – q)× (p+q)= 2(p×q)

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Q: Is z(√2) isomorphic to z(√3)?

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Q: 0) For the POynomial below, 2is a zero of multpliclty two t IS a zero of multplicity wo h(x):メ4+x2-…

A: Given problem:- For the polynomial below, 2 is a zero of multiplicity TWO   h(x)=x4 +x2 -36x +52…

Q: if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

A: (A|b) is the augmented matrix formed by placing elements of matrix B to the right of elements of…

Q: 2. Find the interpolating polynomial using NDD of the points (0,0) , (1,16) , (2,48), (4,88) and…

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Q: z+1

A: Given: z+1z2+12 Let, fz=z+1z2+12 Or, fz=z+12z2+12 The zeroes of f(z) are given by:…

Q: It is possible to write xk as a linear combination of Chebyshev's polynomials, for example %3D…

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Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

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Q: The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A…

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Q: Find the zero-divisors of Z6.

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