Let F be a field and X space = Fn show that Fn is a Hilbert

Q: 19. The 68-95-99.7 Rule. A set of test scores is normally distributed with a mean of 100 and a…

A: Note: As per instruction solving D-FGiven information,population mean = = 100Population standard…

Q: Evaluate the commutators of the operators (a) d/dx and 1/x, (b)d/dx and x2.

A: Given:  a)  ddx and 1x b) ddxand x2 To Find: Commutator of the operators

Q: be a field and let c,d e F. Show that c · (-d) = -(c d).

A: Associative Property of Field F for a,b,c∈F a·b·c=a·b·c

Q: Let x, y ∈ F, where F is an ordered field. Suppose 0 < x < y. Show that x2 < y2.

A: multiplying by x and y in x&lt;y respectively and then comparing both result.....

Q: If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-3)g(-3)…

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Q: Use direct prove to prove that for any two positive numbers x and y, x+y Vxy s 2

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Q: Show that /I +x 0.

A: Mean value theorem: Let f be a function satisfying the following properties: 1. f is continuous on…

Q: Let F(a) be the field described in Exercise 8. Show that a2 and a2 + a are zeros of x3 + x + 1.

A: Given: Fa is a field. To show: a2 and a2+a are the zeros of x3+x+1.

Q: 5. Find the measure of one exterior angle of a regular decagon. a) 36⁰° b) Hº c) 45° d) HH0° 6. If…

A: We need to solve polygon problem.

Q: find all real such that 12x-11>x

A: The inequality can be calculated using absolute values. The absolute value function takes a positive…

Q: evalnante the folobwing integrationollowing a fferent Path C I'm troid.cpathz pathi Re (3,-2) path3

A: Note:- For part (3) it is not clear that the term written with sint (or coefficient of sint ) is "I"…

Q: O Prove that f-1of = ldom / iff f-1 is a function from ran f to dom f.

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Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: b) Prove that if x <y and z<w, then x+z<y+w.

A: Given: Suppose x&lt;y and z≤w. To prove: x+z&lt;y+w.

Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

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Q: (6) Let F be a field and x € F. Prove that -(-x) = = X.

A: Solution: Given that

Q: ABCD is a parallelogram. Find the indicated values: A 20 B 14 C 729 15 10 112° E 40° D (o BE = DE =…

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Q: evalicante the folining inregratio n , falliwing diffoit PathC Im to.). (3,!), parhz Pathe Re (3,-2)…

A: The given problem is to evaluate the complex integral over the given path z= 3+cos(t)+i sin(t) for t…

Q: Linear Alegbra and Differential Equations

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Q: Consider the system below. * = rx + y – x³ jy = -x + ry – 2y Chis system has a fixed point at (0,0).…

A: First we will calculate Jacobian matrix at the origin and then its eigenvalues. Then depending on…

Q: If F = Za[z] (z²–cz+1) find the value of c for which F will be a field? %3D

A: F is field iff x2-cx+1 is irreducible over f.

Q: %31 -I(x) Prove that Bassel function

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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: Let F be a field and let a, b e F. Show that (-a) - b= -(a - b).

A: Introduction: Associative property of field F for a,b,c∈F. (a·b)·c=a·(b·c)

Q: Let A= R- {o,}. det G = {4, t, qf where 1: A> A defined by icx)> x z¢A L+ ズ-A fex) = 1ーメ+x-A 1-X 9:A…

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Q: = Let p¹²-2x+1, p² = 3 +3x+1 and p35x + 10. Let = x³-3x + 4. Is q in me span of pl,p2 and p3?

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Q: Show that gcd (f1,f2,f3) = gcd(f1, gcd (f2,f3)), where each fi is a polynomial in some field F[x]

A: We prove here that gcd (f1,f2,f3) = gcd(f1, gcd (f2,f3)), where each fi is a polynomial in some…

Q: Let x &gt; 0 and b &gt; 0. Show that

A: