9. discuss the behavior of the dynamical system xk+1= AXk where-0.3]2 ] (b) A =1.5(a) A = 1.20.30.41-0.3 1.1

Stability of a system is determined from the eigenvalues. The eigenvalues of a matrix corresponding…

Answered: 9. discuss the behavior of the…

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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1. Find y by Cramer's rule for the following linear system. x+Oy+2z 6 -3x+4y+6z= 30 --2y+3z%=8 rallclenined with sides F(1,-3. -1).
3. In M3x2(F), prove that the set { ( ) ( ) ( ) ( ) ( ) } " 0 0 1 is linearly dependent.
9. P = 15 -4 -7 2e31 – 8e- -4e31 + 2e- ž(1) = | 3e3t – 20e- -6e31 + 5et Show that x1 (t) is a solution to the system x = Px by evaluating derivatives and the matrix product -4 ž(1) = | 15 -7 Enter your answers in terms of the variable t. Show that x2(t) is a solution to the system x' = Px by evaluating derivatives and the matrix product 9. 3(1) = | 15 -4 X2(t) -7 Enter your answers in terms of the variable t.
Activity 2: By applying Kirchhoff's current law in an DC circuit with three nodes. The three nodes' voltages (V₁, V₂ and V₂) can be characterized by the following equations: 5V₂ + 2(V₁ - V₂) + V3-24 = 0 2(V₂-V₁) + 4V₂ + (V₂-V₂) - 12 = 0 (V3-V₁) +2(V₂-V₁) = 0 (2-A) Rearrange the above three equations into a standard matrix form. (2-B) Find V₁, V2, and V3 using the inverse matrix method. (2-C) Find V₁, V2, and V3 using the Gaussian elimination method. (2-D) Verify your answer using MATLAB.
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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9. discuss the behavior of the dynamical system xk+1= Axk where (a) A = |"1.2 0.3 1.5 -0.31 0.4] a) A = [2 (b) A = -0.3 1.1]