Solve the system Ÿ' = AŸ + Ğ for A = and Ĝ = 5z 3 as follows: (a) Verify that A is similar to B= with similarity matrix P = (b) Find a fundamental matrix MB of solutions to the equation Z' = BŽ (c) Find a fundamental matrix MA of solutions to Ÿ = AỸ

Solve the system Ÿ' = AŸ + Ğ for A = and Ĝ = 5z 3 as follows: (a) Verify that A is similar to B= with similarity matrix P = (b) Find a fundamental matrix MB of solutions to the equation Z' = BŽ (c) Find a fundamental matrix MA of solutions to Ÿ = AỸ

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

i need the answer quickly
(9) If 2 0 0 1 3 A-'B-1 and A = 2 -1 evaluate the matrix B.
then the standard matrix of T is A = 20 17 38 -17 20 T ([³]) = [²9] 38 ¹ ¹([^]) = [³] · and T
Find a 3 x 3 matrix A whose -4-eigenspace is and whose 3-eigenspace is A = V = {(x, y, z) in R³ | -8x14y + 10z = 0} 8pc (C) {}} W = Span
If A has column 1 + column 2 = column 3, show that A is not invertible:(a) Find a nonzero solution x to Ax = 0. The matrix is 3 by 3.(b)Elimination keeps column 1 + column 2 = column 3. Explain why there is no third pivot.
A=30 ,B=20, C = |,D= 22 Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes an angle at +D degrees (counterclockwise) from the x-axis.
Find the change of basis matrix from B₂ to B₁. B₁ = = -13/11 31/22 -12/11 -2 CUEROOL) {}} B2 = -2 1 1 20/11 -57/22 21/11 4 -2 |-2/11 -35/22 10/11 1 4 5 1
Write the given second order equation as its equivalent system of first order equations. u" + 5u' + 7u = 0 Use v to represent the "velocity function", i.e. v = Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u'(t). u' = Now write the system using matrices: u d dt V
-2 Q2: A) If A' = and the det = -2 -1/2] find the matrix A and what is the rank of this matrix ? B) Solvė the following matrix equations for x,y and z x 3 - y [3 71 - XJ
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 + x₂ + x3, x2 = - 13x₁ - 7x₂ -X3, X'3 = 13x₁ + 13x2 + 7x3 * A What is the general solution in matrix form? x(t) = Jiry
G1/ Find A' of the matrix 3 -1 A = %3D 2. -4
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)