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 = 7x₁ + 7x₂ + 4x3, x'2 = -6x₁ - 6x₂ - 7x3, x′3 = 6x₁ + 6x₂ + 7x3What is the general solution in matrix form?x(t)=

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Answered: The eigenvalues of the coefficient…

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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Find the eigenvalues of the coefficient matrix for the system.
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply eigenvalue the system. the method to find a general solution of x₁ = 3x₁ + x₂ + 3x3 2 x ²₁ = x₁ + 5×₂ + x ₂ 3 x3 = 3x, +×ъ+ 3x3 What is the general solution in matrix form? x(t)=
By using the method of least squares, find the best parabola through the points: (-1,-3). (1,3). (-2,-3). (0,-3) Step 1. The general equation of a parabola is c₂+₁+c₂2²-3. Plugging the data points into this formula gives a matrix equation Ac=y. 1 ATA- ATy= 1 Step 3. Solving the normal equation gives the answer -8 which corresponds to the formula a Step 2. The matrix equation Ac=y has no solution, so instead we use the normal equation A¹A = A¹y O 0 3
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 = 4x₁ + 3x2+4x3, x'₂ = 3x₁ + 5x2 + 3x3, x'3 = 4×₁ + 3×2 + 4x3 What is the general solution in matrix form? x(t)= C₁ + 3C2e111 + C3e2t -4c2e111-2c3e21 11t -C₁-11c2e +
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) =
Compute the matrix exponential eat for the system x' = Ax given below. x₁ = 41x₁40x2, x 2 = 38x₁ - 37x2 1 eAt (Use integers or fractions for any numbers in the expression.)
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) =
Find the general solution of the following inhomogeneous systems. Use either eigenvector decomposi- tion or undetermined coefficients method. These problems can be solved by hand, but you can also use technology to assist you at any stage. When using technology always report on what function you use. **BHRAIBHS] -2 5 5 -2 (a) = (b) + = 2 -1 **[G]HBKH[**] 3 -2 3e + -2t cos 3t
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) =
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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 = 7x₁ + 7x₂ + 4x3, x'2 = -6x₁ - 6x₂ - 7x3, x′3 = 6x₁ + 6x₂ + 7x3 What is the general solution in matrix form? x(t) =