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Linear Algebra With Applications
Found in: Page 324
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

We are told that [1-1-1] is an eigenvector of the matrix [411-50-3-1-12] what is the associated eigenvalue?

Hence, the required eigenvalue is λ=2

See the step by step solution

Step by Step Solution

Step 1: Definition of the Eigenvectors

Eigenvectors are a nonzero vector that is mapped by a given linear transformation of a vector space onto a vector that is the product of a scalar multiplied by the original vector.

Step 2: Finding eigenvalues

Consider x=1-1-1 be an eigen vector of the matrix 411-50-3-1-12.

The objective is to find the associated eigenvalue.

If x is an eigen vector of A then Ax=λx where scalar λ is called an eigenvalue of A.


Ax=λx411-50-3-1-12 1-1-1=λ1-1-1 411-50-3-1-12=λ1-1-1 2-2-2=λ1-1-121-1-1=λ1-1-1

Hence, the associated eigen value is λ=2

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