If A is normal and no singular prove that so also is A-1

Q: a – b -| < 1, if|a| < 1, and |b| < 1. 1- āb - Show that|-

A: From the given information. For , then show that .

Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

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Q: Find all a so that A = α 1 -1 1 2 1 -1 1 is positive definite. 4

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Q: Prove that if H has index 2 in G, then H is normal in G.

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Q: S S-a₁ + S S-a₂ ++ n² ≥ S-an n-1' S ZZUA

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Q: Suppose X and Y have joint characteristic function (s, t). Show that, subject to the appropriate…

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Q: Prove that z =z iff z is real.

A: z represents a complex number which is in the form x+iy, where x and y are the real numbers and i is…

Q: Prove that d(A) = Ø if and only if A is both open and closed.

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Q: Let n > 3 where x, y , z € R", |x – y| = d > 0, and r is some positive real number. Prove that if 2r…

A: It is given that x and y are d distance apart and r&gt;d/2 where x, y, z belongs to Rn So locus z…

Q: Let f(x) = a,x" + a, p* + ...+ a, E Z[x] and a, + 0. Prove that if r and s are relatively prime…

A: It is given that,  f(x) = anxn + an-1xn-1 +...+ a0 ∈ ℤx  with an ≠ 0. Also, it is given that r and s…

Q: Let a, b € Z with a | b. Prove that an | bn for every positive integer n.

A: Given that           a, b∈ℤ with a|b. To prove an|bn  , we shall use mathematical induction.

Q: Let α belong to Sn. Prove that |α| divides n!

A: The symmetric group ​ is the group of permutations on n objects. Its order is .

Q: Prove that ||A||1 = max1<j<n{£", |aij|}. %3D

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Q: Find gcd(2,3+5i) in Z[i]

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Q: Prove that, IXI<a Rf and If -aL X Z a

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Q: (B) Prove that (Q,|·|) is not complete.

A: A metric space (X,d) is said to be complete iff every Cauchy sequence in X converges to a point in…

Q: 3. Prove that if a 0.

A: To prove that if a&lt;0 and b&lt;0, then ab&gt;0.

Q: x₁ + x₂ + +x. Prove that -x₁)(1+x₂)... (1+x) ≤1+S+ ... S² S³ + 2! 3! +...+ uS - n!

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Q: Let p be prime. Prove that if H ≤ G, |G| = 2p and H is not normal, then |H| = 2.

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Q: Prove, without using any results from the chapter notes, that for all z = C, z² = 2².

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Q: Let n E Z. Prove that 3 n if and only if 3 | (n² - 1).

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Q: A = 1 - 2 3 k 0 1 2 -k -4

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Q: (2 Let xinN(0.1), n = 2 and T= Xx +X2 Show that Tis a Sufficiency Stakistic.

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Q: 1 real number such that a+ E Z. Prove that a" + 1 E Z for any n E N. Let a be any

A: Given that α+1α∈ℤ where α∈ℝ. To prove that αn+1αn∈ℤ for any n∈ℕ , use the method of induction. That…

Q: Prove that if a < 1 and [b] < 1. a -b = 201₁ āb 1 <1

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