Show that the norms 11·11 and 111:111 art =cquivalent if and only if sup{||||||:|1x|| = I} CAD and inf{111X/1) : 11x1) = 1²} 20₁

Q: Find all solutions for x, up to congruence.  x ≡ 2^63 (mod 61).

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Q: e (se (17))

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Q: 2. Let f(x) = x - 5 and g(x) = x² +3x. a) Find (f + g)(x) b) Find (f – g)(x) c) Find (f g)(x) d)…

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Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: Show that if x+yi=(a+bi)- is true, then x-yi=(a-bi)-is all real numbers). true (x, y, a, and b are

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Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Let Sy := {1-(-1):NEN. Find iNf Sy and sup Sy

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Q: Find gcd (356250895, 802137245). Write it as 356250895x + 802137245y for x, y in Z. Show work.…

A: The objective of this question is to find the greatest common divisor (gcd) of 356250895 and…

Q: h9HXth*x f3.1) he mt itextsS St ,2)

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Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

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Q: nd the supremum and infimum of the set D defined by D:= :neN

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Q: ind all solutions of the linear congruence: 9x = 5 mod (14)

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Q: Prove that if b and c are odd, then a bc = a a ()) b C

A: Using definition of Jacobi symbol