Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: Show that MnXn and Rn^2 are isomorphic.

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Q: is not isomorphic to Qi Show that (R. +) (R-1R , )

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Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

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

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Q: Find a counterexample to Lie's Theorem when k is not algebraically closed and chark = 0. %3D

A: According to Lie's theorem, for any finite-dimensional linear representation of a finite-dimensional…

Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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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: こ be terms Prove Find o of ů, ů. your resubts . in

A: Consider the given vectors: Here the objective is to find the vector w such that

Q: Show that R is not compact.

A:

Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: xy If z show that: x- y

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Q: Find the infimum and supremum of the set X = {3 – Vztn ine N}. -

A:

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

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Q: is the gropt Q whch of Hhe of followring

A: Given that: 1. y=x2ex2. Graph of f(x)

Q: Prove using the IVT. 2x = bx has a solution if b > 2.

A:

Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

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Q: Let xe" and yer show that <xiy)=ytx is on imer product %3D

A: We have to show that &lt;x,y&gt; = y*x is an inner product

Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: Prove that d (sec"x)= 1.

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Q: Hew.b prove that CAXB)-Ais atways-Zero

A: Topic:- vector  algebra

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: Prove that z'e'-z = 1 has exactly two roots inside the circle |z] = 1.

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Q: lar, let m = 2 and n e of A and B such that

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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: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: show by of R then IUI is not ideal example if In and Iz are icdeals an

A:

Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: prove that esch'x - In (* + x2 %3D

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Q: IRI- 2. <| sinz|< -e 2

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Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

A:

Q: Show that K, is not planar.

A: To prove: K5 is not a planar graph. Proof:  This is proved by the method of contradiction. We use…

Q: Let H = Span{1+x,1+x², 3+x +2x², 2 + x + x²}. what is dimH?

A: Solution

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

A:

Q: -3 [-1+v3i]

A: Explanation of the answer is as follows

Q: Find all triples of integers (x, y, z) that satisfy x² + 2y² = z2.

A:

Q: /show that fo-1x is-Contindals everywhere.

A:

Q: Let X1,..., Xn be Show that Y = min(X1,. %3D Show that

A: From the given information, X1, X2,.....,Xn are independent, Xi~expλi The density function for Xi…

Q: Prove the following: %3D

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Q: Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the…

A:

Q: What theorem shows that GTY = GUX? Osss O SAS O AAS O ASA

A: We have to check

Q: -x+y<y. 2 If x < y, prove that x <

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Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

Q: 10. Prove that the set H={[,ne subgroap of GL(2, R). For show that x HxcH but xHx+H. :9 GL(2,R),

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Q: Find a bijection between the interval (−1, 1) and R.

A: