Given the sets A and B below, prove or disprove each of the statements that follow. A = {n € Z | n = 4a - 3, a € Z} B = {n € Z | n = 12b + 7, b € Z} a) ASB

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Q: Exercise 5.5.8 Explain why an nxn matrix A is both one to one and onto if and only if its rank is n.

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A: We have to write the series for  f(x)=sinh(x)

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Q: η Σ() = 2 – n+2 2n

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Q: 1. Show that the series COS X 1 + cos 3x 3 is convergent whenever x is not an integer multiple of .…

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Q: = Given that the matrix A has eigenvalues X₁ = 1 with corresponding eigenvector ₁ = = and X₂ = -4…

A: We use definition of eigenvalue and corresponding eigenvector of matrix A.

Q: From smallest to largest, the eigenvalues are A₁ <A₂ < X3 where X₁ 1₂ 5 X3 = Find the eigenvalues…

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Q: 6 0 1 3 -2 0 -8 0 -3

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Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

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A: The given equation is, y=f(x)=ax4+bx3+cx2+dx+e. To Find: Values of a,b,c,d,e If slope is -24 at x=3…

Q: 1) Make a change of variable so that the following series begins with k = 5. n i=2 (−1)²+1 (i-1)²

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Q: s2

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Q: Find eigenvalues and eigenfunctions of the boundary value problem x²y" = xy, y(1) = 0, y(2) = 0.

A: x2y''=λy,     y1=0,    y2=0

Q: Question: 7. A small country consists of 7 provinces with the populations according to the table…

A: Given: Province Population A 25312 B 19734 C 33407 D 29591 E 13288 F 22751 G 31992…

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A: Note: We will be solving pat (B) as asked. Given matrix is: Q=131141321413-314 We need to find the…

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A: We have to evaluate: ∫0.121xdx using the trapezoidal rule. Also, take n=8. And approximate value =…

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Q: If we call the Fourier transform of x(t) as X (w), what will be the Fourier transform of (e^bt)x(t)

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Q: Let f : Z5 ! Z5 be a function by f([a]) = [3a + 2]: (a) Show that f is well-de ned. (b) Determine…

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Q: Give the equation for the function which would have graph shown below. Use f(x) for the output.

A: We can find the equation of the given graph.

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Q: a. C. 2 1²2 [132] 0 b. 2 d. -2-1

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Q: Solve the initial value problem below using the method of Laplace transforms. y"-3y'-18y = 0, y(0) =…

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