Explanation Given: The matrix is, A = [ 2 x 1 − 5 ] The eigenvector is, u = [ 1 − 1 ] . Approach: For an ( n × n ) matrix A , find all scalars λ such that the equation A x = λ x has a nonzero solution, x . Such a scalar λ is called an eigenvalue of A , and any nonzero ( n × 1 ) vector x satisfying the equation is called an eigenvector corresponding to λ . The eigenvectors corresponding to an eigenvalue λ of A are the nonzero solutions of ( A − λ I ) x = 0 . Calculation: Assume λ be the eigenvalue of u . Write the matrices in the form ( A − λ I ) u = 0 , [ 2 − λ x 1 − 5 − λ ] [ 1 − 1 ] = [ 0 0 ] Calculate the above matrix

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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Chapter 4.SE, Problem 12SE

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The value of $x$ and the eigenvalue $λ$ for the given eigenvector $u$ .

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The value of x and the eigenvalue λ for the given eigenvector u .

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The value of $x$ and the eigenvalue $λ$ for the given eigenvector $u$ .

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The value of x and the eigenvalue λ for the given eigenvector u .

Solution Summary: The author explains how to determine the value of x and the eigenvalue lambda for the given.

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The value of $x$ and the eigenvalue $λ$ for the given eigenvector $u$ .