Prove that the trivial G is faithful if and only if G = {1G} representation of a nite group
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Q: Solve the equation [2] = +s LOJ +t (0) -8x + 3y - 7z = 4.
A: The Given equation is -8x+3y-7z=4 ......(1)
Q: prove v(x1) = v(xn) → x1 injective if x1 ‡xn → v(x1) ‡ v(xn) v →x1 = xn ⇒
A: To prove: vx1=vxn→x1=xn⇔x1≠xn→vx1≠vxn
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A: Let length of the printed page be 'x' inch and breadth is 'y' inch. Now Given that…
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Q: Let A; be elements of T for i E I. Show that Uiel A¡ E T.
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Q: Find the Taylor Series, up to and including quadratic terms, of z=f(x, y) = ln(ry³1) about the point…
A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…
Q: Explain: why it is show steps, please explain each part( no table) (~P VQ) ^ (~PVR) =~PV QAR
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Q: 2.Let a be a unit speed curve lying on a sphere center c and radius a > 0. Find the minimum value of…
A: Given That : Let α be the unit speed curve lying on a sphere center c and radius a>0. To Find :…
Q: ) Find all the values of x such that the given series would converge. (-1)"x" 11"(n² + 11) The…
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Q: Let φ1(x) = 1, φ2(x) = x/|x|, φ3(x) = x^2 − 1/3 for −1 ≤x ≤1. Show that (φ1,φ2,φ3) form an…
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Q: If o< p < 1 then IP is avector space but is not anorm for || X | p = ( ≤ n || Xn llP) to ท яр
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Q: If ß represents the number of units of change in y for every one- unit change in x (i.e. the slope)…
A: We need to rank the slopes of the lines: I, II, III, IV from most negative to most positive.
Q: dy senx+y cos x = xsenx dx y(7/2)=2
A: Let us consider a differential equation of the form, dydx+P(x)y=Q(x) Then solving the equation…
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Q: From which we have (a₁ + a2) D+ (a3 + a4 + α5) d-(1 − A) (B₁ + B₂) D² = (1 − A) (B3 + B4 + B5) Dd…
A: Given: D1-A=α1+α2D+α3+α4+α5dβ1+β2D+β3+β4+β5d . . . (1)andd1-A=α1+α2d+α3+α4+α5Dβ1+β2d+β3+β4+β5D…
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A: The metric is: d:R2×R2→R0+; x=(x1,x2), y=(y1,y2)∈R2d(x,y)=min{|y2-x2|,1}if x1=y11otherwise…
Q: Q.5 Consider the Sturm-Liouville problem d x(xy')+(2-1)y=0, dx y'(1)= 0, y'(e)=0
A: Given, xddxxy'+λ-1y=0, y'(1)=0, y'(e2)=0
Q: 2) a) Let T: C² C²: Ty = [x+2y-iz] 2y + iz Lix+z-2z Find [7] B [7] B and P where
A: Given information T : C2 →C2T xyz = x+2y-iz2y+izix+z-2z simplify it, T xyz = x+2y-iz2y+izix+z-2z…
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Q: 33. Suppose V is known to have dimension k. Prove that (a) any k independent vectors in V form a…
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Q: 1. (x(t), y(t)) DETAILS Use variation of parameters to solve the given nonhomogeneous system. dx dt…
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Q: 5 (a) Find all solutions of each system of linear equations: x-3y - 22 7 2x - 5y + z = 5 -x+4y+62 =…
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Q: A flowerbed is decorated with four concentric circles of flowers, in such a way that each circle…
A: To solve this problem we use basic algebra .
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Q: Determine the average rate of change of f(x)=3(2)" on the interval 0<x<2. a) 4. Ax b) Ax d) = 45 c)…
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Q: Let (X, T) topological space, where X = {a,b,c,d} and T = {X. Ø, {a}, {a,b}, {a,b,c}} Find a) Basic…
A: Given that X, T topological space, where X=a, b, c, d and T=X, ϕ, a, a, b, a, b, c.
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A: 1). A set ∅ is known as an Empty Set (i.e., a set having no elements). Here P({∅}) is the power set…
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Q: For which vectors (b₁,b2, b3) do these systems have a solution? X1 b₁ 1 1 1 X1 HO-N-HD-B b2 and 0 1…
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Q: 50. (Recommended) Suppose all vectors x in the unit square 0 ≤ x₁ ≤ 1,0 ≤ x₂ ≤ 1 are transformed to…
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Q: Let fbe a continuous function on an open subset U of a Banach spe into a Banach space Y. Let a and b…
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Q: b. Let A and B be elements in Sn T. Show that An BE S N T. c. Let A¡ be elements of SnT for i € I.…
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Q: Which of the following statements are equivalent? Proof your result. P→ (QR) (P→Q) ^ (P→ R) (PAQ) →…
A: Introduction: When identical statement variables are used to denote the component statements, two…
Q: Verify that the set C[a, b] of all continuous real-valued functions defined on the interval a ≤ x ≤…
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Q: Which of the following statements are equivalent? Proof your result P→ (Q→R) ! (P→Q) ^ (P→ R) (PAQ)…
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Q: A long jumper leaves the ground at an angle of 21° above the horizontal, at a speed of 9 m/s. The…
A: (a) The height of the jumper is modeled by the equation, hx=-0.046x2+0.363x For the horizontal…
Q: Find all the values of x such that the given series would converge. 5" (x")(n+1) (n + 11) The series…
A: 1. Given series is ∑n=1∞5nxn(n+1)n+11 By Ratio test we get limn→∞5n+1xn+1(n+2)n+12×n+115nxn(n+1)…
Q: Using two steps of the Gauss- Seidel method, find an approximate solution to the problem Ax=b where…
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Q: prove Øx = Øy for X, Y Øx = {x & X: x # x x} øy = {y&Y: y = y}
A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…
Q: Determine the Fourier series expansion for f(x): f(x) = x, XER, -T≤x≤T f(x) = f(x+2π)
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Q: Please teach how to solve not just solve (concepts) | Prove that: a) b) if X-1 exists, then it is…
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Q: Verify that the set C[a, b] of all continuous real-valued functions defined on the interval a ≤ x ≤…
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Q: dy dx y x y (1)=e-1 xe*
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- 16. Suppose that is an abelian group with respect to addition, with identity element Define a multiplication in by for all . Show that forms a ring with respect to these operations.Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.24. Prove or disprove that every group of order is abelian.