Problem 4. Let A =You are given that (2 – A) ( –- X) is the characteristic510polynomial of A.Find the eigenspace E2.Without any more calculation, find the eigenspace E1.Sketch the phase portrait for the discrete dynamical system 7(t + 1) = AF(t).Describe all possible ão for which lim00 7(t) = lim;→∞ A'ão equals 0.Let A = A+ kI2. Consider the discrete dynamical system ī(t+1) = Ak7(t).(b)For which k is 0 an asymptotically stable equilibrium for this system?

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Answered: 4 Problem 4. Let A You are given that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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10. (BH) Let L : P + P2 be defined by L(p(e)) = zp'(2) dz, and let E = {1,t} and E2 = {1,t, t} be the standard bases for Pi and P2. (a) Find the matrix A associated with in these bases. (b) Find £(3t – 1) directly and using A.
Part d only
In the following system Problem, categorize the eigenvalues and eigenvectors of the coefficient matrix A and sketch the phase portrait of the system by hand. Then use a computer system or graphing calculator to check your answer. x'1 = 50x1 - 20x2, x'2 = 100x1 - 60x2
In the following system Problem, categorize the eigenvalues and eigenvectors of the coefficient matrix A and sketch the phase portrait of the system by hand. Then use a computer system or graphing calculator to check your answer. x'1 = x1 - 5x2, x'2 = x1 + 3x2
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3. Given the model 1 4 1 xt=3t-1-3-2 + Wt − Wt-1 + 4Wt-2, where we is white noise. (a) Determine if the model is stationary using the lag operator B. (b) Determine if the model is invertible using the lag operator B. Write the model in ARMA(p, q) notation. Write the model in ARIMA (p, d, q) notation. (e) Which of the two models above is preferred? Give one reason.
For the system of equations ()- dæ -3 -1 x. dt 1 1. Find the eigenvalues and eigenvectors of the matrix. 2. Find the coordinate transformation that will put the equation into canonical form and show that this works. 3. Write down the general solution.
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For the matrix Z below, find the eigenvalues and eigenvectors. a. 1 0 -2 Z = 0 5 (-2 0 4 b. Verify if the function below is a linear transformation or not. T:P: →R defined by T (a + bx + cx³) = [2a – b - i. b+c] ii. L: R →R' defined by L = xy| Given the following transformation L(u)=Au, where u = (x, y) and the standard (or induced) с. matrix A is given as A i. Sketch the triangle connecting the points (2, -2), (2, -5) and (5, -2). Then sketch its transformation image if u represents the poit. ii. Identify the type of transformation shown above?
Please help me the first 3 parts. Part A part B and part C. Please make sure type by computer although

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4 Problem 4. Let A You are given that (2 – A) ( –1) is the characteristic 10 polynomial of A. (a) (b) (c) Find the eigenspace E2. Without any more calculation, find the eigenspace E1. Sketch the phase portrait for the discrete dynamical system 7(t + 1) = AF(t).