Solve. The same way to ask the solutionFind a fundamental matrix of the following system, and then apply x(t)=(t)(0) x to find a solution satisfying the initial conditions.x'=-3 -29 3x, x(0)=B. -1+2t -3-2e-3t2 cos 31- 2 sin 3t(t)=-3 cos 3t+3 sin 3t 3 cos 3t+ 3 sin 3t3 cos 3t 2 sin 3t-2 cos 3tOD. (t)=2 sin 3t+3 cos 3t-3 sin 3tFind a solution satisfying the given initial condition.x(t)(Use integers or fractions for any numbers in the expression)44This is a solved questionFind a fundamental matrix of the following system, and then apply x(t)=(t)(0) x to find a solution satisfying the initial conditions.x'=-6-236 6x, x(0)=Exze2 cos 6t- 2 sin 6tc. (t)=-6 cos 6t+6 sin 6t 6 cos 6t+ 6sin 6t6e-6t-2e-6tOD. (t)=-2 est6e-6tFind a solution satisfying the given initial condition.3 cos 6t-2 sin 6tx(t) =-3 cos 6t + 15 sin 6t(Use integers or fractions for any numbers in the expression.)

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Answered: Find a fundamental matrix 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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b) A system of differential equation is given as follows: x₁ = 9x₁ - 4x₂ x₂ = 8x₁ - 3x₂ where x₁ and X2 are functions of . Given that the eigenvalues of A= and 5 with the corresponding eigenvectors i) Write a matrix P that diagonalizes A. ii) Write a diagonal matrix D such that P¹ AP = D. iii) Hence, find the general solution to the system. [4=[83] are 1 and respectively.
dx dt = x+y+z; (a) (b) dy dt = x + 3y - z; dz dt = 2y + 2z For the system above, define matrix A and vector X and write the system in matrix form. Show all work to solve the system and clearly state the general solution vector X
Find a fundamental matrix of the following system, and then apply x(t) = (t)Þ(0) 1x to find a solution satisfying the initial conditions. -6-2 x' = X, X(0)= (0)-[1] 36 G 1+2t - 6-2 e-6 2 cos 6t - 2 sin 6t C. (t)= - 6 cos 6t + 6 sin 6t 6 cos 6t + 6 sin 6t 6e - 6t -2 e-6t D. Φ(t) = -2e , 6t 6 e-6t Find a solution satisfying the given initial condition. x(t) = ¯ (Use integers or fractions for any numbers in the expression.)
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 5x+6y=0 y" - 5x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? O A. x₁ = x¹, x₂ =y' O B. X₁ =X, X₂=X', X3 = Y, X4=y' OC. x₁ = x, X₂=x", X3 = Y. X4=y" OD. x₁ = x¹, x₂ = x¹, x₂ =y', X4=y" Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. O B. X₁ X₂ x₁² X1 x2 x3 X4 X1
2x + 3y + 6z = 3 + 2y + 2z = −1 using 3x - 4y - 5z = -6 B. Solve the linear system-x 1. Cramer's rule 2. inverse matrix 3. LU decomposition
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Express the given system of higher-order differential equations as a matrix system in normal form. x" + 6x + 7y=0 y" - 2x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. X₁ = x¹, x₂ = y' O B. X₁ =X, X2₂=X'', X3 = Y, X4 =y" O c. x₁ = x¹, x₂ = x¹, X3 = y', X4 =y" O D. x₁ = x, X₂ = x', X3 = Y, X4 = y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. B. X₁ X₂ X₁ S w X4 || X₁ X2 x1 3 ... W X4 ро
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If A is an (n x n)-matrix of real constants that has a complex eigenvalue and eigenvector v, then the real and imaginary parts of w(t) = elty are linearly independent real-valued solutions of x' =Ax: x₁(t) = Re(w(t)) and X₂(t) = Im(w(t)), The matrix in the following system has complex eigenvalues; use the above theorem to find the general (real-valued) solution. 0 30 -3 0 0 X 005 x(t) = = x' = Find the particular solution given the initial conditions. x(t) = = x(0) = 123
Let the matrix M be given by sin o CoS O - sin o M = COS O (i) Is the matrix M invertible? (ii) Calculate M-1 if possible.

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