Consider the initial value problem for the vector-valued function x, -1 x' = Ax, A = 1 x(0) = Find the eigenvalues A1, A2 and their corresponding eigenvectors v1, V2 of the coefficient matrix A. (a) Eigenvalues: (if repeated, enter it twice separated by commas) d1, A2 = 1, 1 Σ (b) Eigenvector for A1 you entered above: V1 = <1,1> Σ (c) Either the eigenvector for A2 you entered above or the vector w computed with v, entered above in case of repeated eigenvalue: 1 Either v2 or w = <0, -1> Σ (d) Find the solution x of the initial value problem above. x(t) = Σ Note: To enter the vector (u, v) type .

Consider the initial value problem for the vector-valued function x, -1 x' = Ax, A = 1 x(0) = Find the eigenvalues A1, A2 and their corresponding eigenvectors v1, V2 of the coefficient matrix A. (a) Eigenvalues: (if repeated, enter it twice separated by commas) d1, A2 = 1, 1 Σ (b) Eigenvector for A1 you entered above: V1 = <1,1> Σ (c) Either the eigenvector for A2 you entered above or the vector w computed with v, entered above in case of repeated eigenvalue: 1 Either v2 or w = <0, -1> Σ (d) Find the solution x of the initial value problem above. x(t) = Σ Note: To enter the vector (u, v) type .

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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Question

Consider the initial value problem for the vector-valued function x,
-1
x' = Ax,
A =
1
x(0) =
Find the eigenvalues A1, A2 and their corresponding eigenvectors v1, V2 of the coefficient matrix A.
(a) Eigenvalues: (if repeated, enter it twice separated by commas)
d1, A2 = 1, 1
Σ
(b) Eigenvector for A1 you entered above:
Vi = <1,1>
Σ
(c) Either the eigenvector for X2 you entered above or the vector w computed with vị entered above in case of repeated eigenvalue:
Either v2 or w =
<0, -1>
Σ
(d) Find the solution x of the initial value problem above.
x(t) =
Σ
Note: To enter the vector (u, v) type <u,v>.

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