Below are a list of equilibrium points for a system whose Jacobian matrix is given by(21-28x– 15y)42143(24– 3x- 4y)2020Select all of them that are stable.318273(금이)3(0,0)(0,12)1717

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Answered: Below are a list of equilibrium points…

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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2. Find the general solution of the following linear system: X + 3z = 1 Зх + у = 1 None O (-3t + 1, 6t + 1, t) O (-3t + 1, 9t – 2, t) O (i + 2, 1 – 1, t) | 6. (8 – 1, t – 5, t)
U and = span{[-3 4 5],[-11 -2 3]} W = span{[ span{[−4 x = [ UnW = −1 5],[-12 -1 1x×3 of V = R¹×³. Find a matrix X € V such that E 5], [-12 -5 9]} = span{X}.
4. Let -{0-0)-G)} (a) Define an appropriate matrix and apply the rref command to determine if w = 25 55 can be expressed as a linear combination of {V1, V2, V3}. 10 S = {V1, V2, V3} = 3
5 4? What is the determinant of the 6 x 6 matrix whose (i, j)-th entry is x₁y₁
Without the use of a calculator, calculate the determinant of the matrix. 1. 2. -3 7 1 0 -5 -8 0 0 11 0 2 2 7 0 9 -2 0 0 3 7 11 16]
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1. 2. 3. For which values of a and b is the following system of equations inconsistent. x+2y3z = 4 3x = y + 5z = 2 4x + y + az = b (a) a= 2 and b = 6; (d) a = 1 and b = 3; (d) A = Find the standard matrix for the operator on R² which contracts with factor 1/4, then reflects about the line y = x. 0 (a) A = 1/4 0 (₁/11) ( 0 1/4 1/4 ¹/4) 0 (b) a = 2 and b = 6; (e) None of these. (c) a 2 and b = 6; 0 1/4 - (¹/4) 0 (e) None of these (b) A = (e) None of these (c) A = The linear operator T : R³ → R³ is defined by T(x₁, x2, X3) = (W₁, W2, W3), where w₁ = 2x₁ + 4x2 + x3; W₂ = 9x2+2x3; W3 = 2x1 8x2 - 2x3. Which of the following is correct. (a) T is not one to one. (b) T is one to one but the standard matrix for T-¹ does not exist. (c) T is one to one and its standard matrix for T-¹ is (d) T is one to one and its standard matrix for T-¹ is HOLI 0 1 (88) 0 3 0 1 3 3 WIN - WIN 3 0 1 3 1 -4 3 -3 2 -3 1623
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Below are a list of equilibrium points for a system whose Jacobian matrix is given by (21-28x– 15y) 42 14 3 (24– 3x- 4y) 20 20 Select all of them that are stable. 318 273 (금이) 3 (0,0) (0,12) 17 17