1.00.5-1.0-0.5-0.5the given figure is a phase portrait for a system x' = Ax,(a) The eigenvalues of A could be (circle one)i. A1 = 1, X2 = 2ii . λι-1, λ-2iii. A1 = -1, A2 = 2iv. A1,2 = 1±iv. A1,2 = -1± i(b) If possible, give one eigenvector of A (if it isnot possible, write "N/A")):Answer:

For the given figure is a phase portrait for the system: x'=Ax we need to determine (a) the…

1.0 0.5 -1.0 -0.5 -0.5 the given figure is a phase portrait for a system x' Ах, (a) The eigenvalues of A could be (circle one) i. A1 = 1, X2 = 2 ii. λ1 1, λ-2 iii. A1 = -1, A2 = 2 |3| iv. A1,2 = 1+i v. A1,2 = –1± i (b) If possible, give one eigenvector of A (if it is not possible, write "N/A")): Answer:

1.0 0.5 -1.0 -0.5 -0.5 the given figure is a phase portrait for a system x' Ах, (a) The eigenvalues of A could be (circle one) i. A1 = 1, X2 = 2 ii. λ1 1, λ-2 iii. A1 = -1, A2 = 2 |3| iv. A1,2 = 1+i v. A1,2 = –1± i (b) If possible, give one eigenvector of A (if it is not possible, write "N/A")): Answer:

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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the given figure is a phase portrait for a system x' = Ax, (a) The eigenvalues of A could be (circle one) i. A1 = 1, A2 = 2 ii. A1 = -1, A2 = -2 iii. A1 = -1, A2 = 2 iv. A1,2 = 1+i v. A1,2 = -1±i (b) If possible, give one eigenvector of A (if it is not possible, write "N/A"): %3D Answer:
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Given the correct eigenvalues above and the eigenvectors below, what is the general solution of the system: K₁ = (²₁) x² - (- ₁²) X 1 2 X' 2 cos2t X = C₁ (22) e¹ + C₂ (co2) tet -sin2t) )e² sin2t O A (Cost) et + c₂ (sin2t) tet -sin2t. X = ₁ X = C₁ O B 1 (Cost) et + C₂ (cos2t) et 2 -sin2t sin2t. cos2t X = C₁ (0522) e² + c₂ (Sin2t) et -sin2t cos2t) O D
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please type in your hand clearly thank you.
PART 1 (MCQ: 8 Marks): 1. Choose the most appropriate answer. (a) The eigenvalues of the following eigenvalue problem: are given by An = 0 = (1),X = (0),x '0= xY+ „X (A) n², n=0, 1, 2, 3, - - - (C) (na)², n = 0,1, 2, 3, · - . (B) n², n=1,2,3, - - - (D) (n7)², n= 1, 2, 3, · - - (b) At x = 0, the Fourier series of x - 2, = (x)f I 5x > 0 converges to: (A) -2 (B) –1 (D) 1 (c) The solution of the following Cauchy problem: '00 > x > - u(x, 0) = 0, 4 (x, 0) = x, *00 > x > o0- is given by u(x, t) = (A) [(z+ t)? – (2 – t)*] = ct (B) (7 + t) + (x – t)] =: (C) (z +t)² + (x – t)*] = (2² + t*) 1=(9-2) -0+0)은 (a) (d) Let o(x) = x² + x, x > 0. If defines an even extension of ø to the entire real line, then for x < 0, (x) = (C) -a2 +x (A) x² +x X - „x ()