Find a general solution of the system = 4x1 + 2x2, x2 = — Зx1 — х2. The matrix form of the system in is х. The characteristic equation of the coefficient matrix is 4 - 2 = (4 – 1)(-1– 1) – 6 3 -1 - A = 12 – 31 – 10 = (1 + 2)(^ – 5) = 0, so we have the distinct real eigenvalues 21 = -2 and 12 = 5. For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes the form [* JD-C) :)-[{] 4 – 2 3 -1- 1 for the associated eigenvector v = [a b]°.

Find a general solution of the system = 4x1 + 2x2, x2 = — Зx1 — х2. The matrix form of the system in is х. The characteristic equation of the coefficient matrix is 4 - 2 = (4 – 1)(-1– 1) – 6 3 -1 - A = 12 – 31 – 10 = (1 + 2)(^ – 5) = 0, so we have the distinct real eigenvalues 21 = -2 and 12 = 5. For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes the form [* JD-C) :)-[{] 4 – 2 3 -1- 1 for the associated eigenvector v = [a b]°.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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