The coefficient matrix A of the 4x4 system below has eigenvalues λ₁ = -6,₂= -3, 236, and 24 = 11. Find the particular solution of this system that satisfies the initial conditions x₁ (0) = 8, x₂ (0) = 6, x3 (0) = 6, x4(0) = 8.x₁ = 2x₁ + x₂ + x3 + 5x4x2 = x₁ + 2x2 + 8x3 + x4x3 = x₁ + 8x₂ + 2x3 + x4x 4 = 5x₁ + x₂ + x3 + 2x4x(t) =

Given information:The system of differential equation is that:Eigenvalues are given as .Initial…

Answered: The coefficient matrix A of the 4x4…

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 matrix 10 -24 -24 -10 has eigenvalues 26 and -26, and corresponding eigenvectors (3,-2) 1 and (2,3) respectively, both of magnitude 1. √13 (a) Write down an orthogonal matrix P and a diagonal matrix D such that PT AP = D. A = 20 1 /13 (b) Use your answer to part (a) to find the standard form of the equation of the non-degenerate conic with equation 10.x² - 48ry - 10y² + 3x - 2y = 0. (c) Hence state whether the conic is an ellipse, a parabola or a hyperbola.
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 3x₁ + x2 + x3, x2 = -7x₁5x2-X3, X3 = 7x₁ + 7x2 + 3x3 What is the general solution in matrix form? x(t) =
The coefficient matrix A of the 4x4 system below has eigenvalues A₁-9, A₂-6, Ag 9, and 4 14. Find the particular solution of this system that satisfies the initial conditions x₁ (0) = 5, x₂ (0) = 5, x₁ (0) = 5, x4 (0) = 5. x₁ = 2x₁ + x₂ + xy + 8x4 x2 = x₁ + 2x₂ + 11xg+X4 X3 X₁ +11x₂ + 2xy +Xg x48x₁ + x₂ + xy + 2x₁ *(t) =
If you have matrix A = [0 1 0; 0 0 1; 1 0 0] and matrix B = Identity matrix, will they have the same eigenvalues because if you swap rows 1 and 3 then rows 2 and 3 of matrix A, you will get matrix B?
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 8x₁ + 3x₂ + 8x3, x'₂ = 3x₁ + 13x₂ + 3x3, x'3 = 8x₁ + 3x₂ + 8x3 What is the general solution in matrix form? x(t)
Consider the following linear system y + The coefficient matrix is known to have eigenpairs (1, H) and (-1,): Use the method of variation of parameters to find a particular solution of this non-homogeneous system.
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x'1 = 4x, + 2x2 + 2x3, x'2 = - 7x1 - 5x2 - 2x3, x'3 = 7xq + 7x2 + 4x3 What is the general solution in matrix form? x(t) =
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x', = 4x, + 2x2 + 2x3, x'2 = - 6x, - 4x2 - 2x3, x'3 = 6x, + 6x2 + 4x3 What is the general solution in matrix form? x(t) =
The matrix 17 0 1 2 2 0 has two real eigenvalues, A₁ = 2 of multiplicity 2, and X₂ = 3 of multiplicity 1. Find an orthonormal basis for the eigenspace corresponding to X₁. -10 -2 -2 A =
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In quantum mechanics, when two states with energies ₁ and E2 mix, the resulting states have different energies E and E, which are the eigenvalues of the matrix H = V (EK). V Choosing to be the state with higher energy, derive expressions for E + E, and E - E in terms of E1, E2 and V.

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