Consider the initial value problem for the vector-valued function x,-14x =Ах,A =x(0)-25Find the eigenvalues A1, A2 and their corresponding eigenvectors v1, V2 of the coefficient matrix A.(a) Eigenvalues:A1, A23, 1Σ(b) Eigenvector for A1 you entered above:V1 =<2,2>Σ(c) Either the eigenvector for A, you entered above or the vector w computed with vj entered above in case of repeated eigenvalue:Either v, or w =<2,1>Σ(d) Find the solution x of the initial value problem above.x(t)ΣNote: To enter the vector (u, v) type .

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Consider the initial value problem for the vector-valued function x, -1 A = -2 x' = Ax, x(0) Find the eigenvalues A1, A2 and their corresponding eigenvectors v1, V2 of the coefficient matrix A. (a) Eigenvalues: d1, A2 = 3, 1 Σ (b) Eigenvector for A1 you entered above: V = <2,2> Σ (c) Either the eigenvector for A2 you entered above or the vector w computed with vi entered above in case of repeated eigenvalue: Either v2 or w = <2,1> Σ

Consider the initial value problem for the vector-valued function x, -1 A = -2 x' = Ax, x(0) Find the eigenvalues A1, A2 and their corresponding eigenvectors v1, V2 of the coefficient matrix A. (a) Eigenvalues: d1, A2 = 3, 1 Σ (b) Eigenvector for A1 you entered above: V = <2,2> Σ (c) Either the eigenvector for A2 you entered above or the vector w computed with vi entered above in case of repeated eigenvalue: Either v2 or w = <2,1> Σ

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 15EQ

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