Q3.(a)If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for(1A2Hence, write down the associated modal matrix P and diagonal matrix D, anduse these values to solve the following system differential equations:* = X1 + 4 x2*2 = 2 x1 + 3 x2%3DGiven that whent 0, x, 0 and x2 2.(b) Use the 4th order Runge Kutta method to solve the differential equation:dye* y%3Ddxfor values of x = 0 (0.2) 0.4 given that y = 1 when x = 0.Give your answers correct to 5 decimal places.Obtain the analytical solution of the differential equation and compare theanalytical solution when x 0.4 with the values obtained using Runge Kutta,

3.(a) The given differential equations are x1˙=x1+4x2…

Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A = Henoe, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: * = X1 + 4 x2 *2 = 2 x1 + 3 X2 Given that whent = 0, x, = 0 and x2 = 2.

Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A = Henoe, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: * = X1 + 4 x2 *2 = 2 x1 + 3 X2 Given that whent = 0, x, = 0 and x2 = 2.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 80E

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