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

Q: a a +1 2² (² + ¹ + x² = 1 [(¹-x)² + (1 + x)² ] F1 2 2 2

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Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

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

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Q: Prove: If a > 0, then (1/a) > 0.

A: It is given that a> 0.It is known that if ab > 0 then a > 0 or b > 0 or a< 0 or b…

Q: . Let A, B = M₁ (F) where n is odd and the characteristic of F is not equal to two. Prove that if AB…

A: AB = -BA.  Take determinant on both sides, we get  det(AB) = det(-BA) = (-1)^n det(BA) = - det(BA) ,…

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: (5a + 6b|a, b = Z} = Z

A: To prove that .Concepts used:Consider two sets  and . To prove that , we first need to show and…

Q: Cg + చ = చ

A: In measure theory, there is a general result known as the additivity of integrals that states that…

Q: Let a e Z. Prove that if 6 | a and 10 | a, then 15 | a.

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Q: (b) Let a.. and m be positive integers. Prove that if (a,m) = (b, m) = 1, then (ab, m) = 1.

A: Given  a, b and m are positive integers.  (a, m) = (b, m) = 1.We have to prove that (ab, m) = 1.

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

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Q: Let S= {n | n=5 k+ 4 for some integer k} Let T= {n|n=5 j– 1 for some integer j}

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Q: 3. Prove that if a 0.

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

Q: Let a, b e C. (i) Prove that if |a| <1 and |6| < 1, then a - b < 1. 1- āb

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Q: Show that if x is in both W and W-, then x = 0.

A: Dot product of perpendicular vectors is 0.

Q: Let a and b be any real numbers such that a 0. Prove that a < b.

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Q: 1) D Prove that 224 O 210

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

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Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

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Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.

Q: Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

A: Suppose A.B = 0 then we have to show that  Column space of B contained in the null space of A  i.e…

Q: Prove that Z Q has the universal property of inverting non-zero elements.

A: in Mathematics, Z is the set of Integers. and Q is the set of all rational numbers. Z→Q Let f(α)=1α…

Q: Prove that Σ(;) = 0.

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Q: Let A = %3D

A: