Theorem 12. Let f be a non-zero continuous function on R uch that f(x+y)=f(x) f(y) ¥x, yER. Show that f(x): =e*, for some constant c±0.

Q: 12. Let xo < x < < x, and let f be continuously differentiable. Show that a f[xo, x₁, x₂] = f[xo,…

A: A continuously differentiable function has a derivative at every point, and that derivative is…

Q: 1 1 -2) 13. Find the rank of A=| 2 1 |and explain why it indicates that A is (-1 -1 2 not…

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Q: 1-x We want to compute dr.

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Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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Q: 19. Is Q[x]/(x² – 6x + 6) a field? Why?

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Q: Explain the Wronskian Derivation?

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Q: Q(4) Find a seel general soluchion of + 16 = 0

A: see below the answer and explanation

Q: Let A = 1 -X -X X 1 -x X X -1 Find x such that A is invertible.

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Q: Let 1 2 A = 3 6 Is A invertible? Explain your answer.

A: To verify is the given matrix A is invertible Or not.

Q: transform is Use Python to find a function whose Laplace 2(s - 1)e-3⁹ s² - 2s + 2

A: import sympy as sp# Define the Laplace domain variables = sp.symbols('s')# Define the Laplace…

Q: 4. V1+ 2 5. V2 - i In Exercises 6 through 8, find irr(a, Q) and deg(a, Q) for the given algebraic…

A: 8. α=2+i   let x=2+i⇒x2=2-1+22i⇒x2-1=22i⇒(x2-1)2=-8 ⇒x4-2x2+1=-8⇒x4-2x2+9=0

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS AND PLS SHOW ALL WORK

A: To perform matrix multiplication in SCILAB, you can use the `*` operator. Below is the SCILAB code…

Q: prove that the covariant derivate satisfies leibniz's rule

A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

Q: PLEASE TYPE ONLY*** Exercise 4.2.3: Find a counterexample. Find a counterexample to show that each…

A: we have to write the counterexample to show that the following statements are false

Q: not use ai please don't

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Q: Use the above to find a quadrature formula of the form f(x)dæ f (x)dx= i=0 that is exact for all…

A: Quadrature formula ∫01x1-x2fxdx=∑i=0naifxi Exact for all fx of degree three. fx=x0,x,x2,x3

Q: By using Caushy Rieman prove that (2) and (3) (2) 4c2) = (3) prove That (3)- 3.

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Q: ;0<x<0, - 0 <0 <0 Let X,,X,X,r(x;e)=- e.w Discuss the sufficiency by using Factorization Theorem.

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Q: One version of the Fundamental Theorem of Calculus can be stated as: q [F(a)adua f(a)da = F(q) -…

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Q: What is the laplace inverse of 5 -3s -7s - S

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Q: Find all monic irreducible polynomials of degree 2 over Z

A: A polynomial of degree 2 in Z3 [x] is irreducible if and only if it has no roots in Z3.

Q: fla) compute T [ f 77E] t.

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Q: Prove the following identity: (x + y)2- (x-y)? = 4xy %3D

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Q: Theorem 6.3. Let a be a real algebraic number of degree n C= = c(a) >0 such that

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Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

Q: La) Emplain why is entive ? the function fcz) = 5z"-6+zcosz -ze

A: z=x+iy⇒5z4=5x+iy4=5(x4-6x2y2+y4)+5i(4x3y-4xy3) ---&gt;eqn(1)⇒xcosz=x cos(x+iy)=x(cosxcos hy-i sin x…

Q: Prove (A → A) → A in H. Note: In addition to the axioms and rule of inference of H, you may use any…

A: ↦(⇁A→A)→A 1. Assume (⇁A→A)→A (Assumption) 2. Assume ⇁A→A(Assumption)

Q: Let 1 2 3 -1 A 4. Compute Ax if (a) x=0 (b) x= (c) x=

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Q: the P to values what tot below A.

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Q: 2 In x 1 e* 2 1 In 2x -1

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Q: a) Factor a +x³ + x into irreducible polynomials in Z2[r];

A: i) Linear factors are irreducible. ii) Just substitute values in Zp and see the expression becomes…

Q: a) Use Newton interpolation to find the unique cubic polynomial f that passes through the points (0,…

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Q: [3.3] Show that (C,+) and (R2, +) are isomorphic.

A: Detailed explanation:We seek to prove a bijective (one-to-one and onto) linear transformation that…