Let [7 -37 A = -4 -1 -6 -2 7 -7 a Define the linear transformation T : R³ → R³ by T(ã) = Aã. Find the images of u = -2 and v = b under T. 3 T(ü) T(7)

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A: The solution is below.

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Q: Consider the following linear maps T: R2 →Rª and S: Rª → M(2, R) defined as follows: 2x + 3y T( %3D…

A: SoT is one to one if T is one one. So we check if T is one one or not.

Q: Solve: L{tet sin 3t} O (18s^2 - 6s + 36) /(s^2 + 2s +10)^3 O (18s^2 +36s 36)/(s^2 +2s +10)^3 (18s^2…

A: Solutions

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A: Given series is ∑n=1+∞10n2+187n2+16n+21

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Q: Find the sum of the given convergent series. > [tan-1(2n – 1) – tan-1(2n + 3)] n=0

A: Telescoping series and converges for the series

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A: F1 : ~X → ~Y      ≈ ~(~X) v ~Y     ≈ X v ~Y F2 : ~X v ~Y F3 : Z ↔ Y     ≈ (Z → Y)•(Y → Z)      ≈ (Z…

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Q: Question 18 Consider f : X →Y,with domain {c, g, 0, e, d, p, 2, U, M, s, n, v} and codomain Y = {69,…

A: 18. Given is a function f from X to Y where, X = {c, g, o, e, d, p, z, u, m, s, n, v}, Y = {69, 10,…

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Q: (-1)" /2n² + 5 Given: power series >) (x + 1)" n=1 Find the interval of convergence of the power…

A: Given series is ∑n=1∞(-1)n2n2+5(x+1)n

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Q: dx x2 -25)2

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Q: 1. Integrate x tan- (x²) dx. x4 + 1 2. (a) Evaluate cos? x sint x dx. (b) Calculate dx. x² – 5x + 6…

A: These are integrals which can be evaluated using standard techniques. The solution typed in LaTeX…

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A: Given question is Let f (x, y) = ln(2x3 − y2) − 4xcos(y − 1) + y a. Fin‎‎d the loc‎‎al linea‎r…

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Q: For all x E R, e* = Ln=0 +0+ n! Express f (x) = x e* as a power series.

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Q: Consider (u, v) = 0 for any vectors u, v e R4. Is this an inner product? Explain why or why not.

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Q: Question 3 Use the method of undetermined coefficients to find a general solution of the…

A: To solve given question first we write the characteristic equation of given differential equation…