Q38E We are told that [1-1-1]聽is an ... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 7: Q38E (page 324)

We are told that $[\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}]$ is an eigenvector of the matrix $[\begin{matrix} 4 & 1 & 1 \\ - 5 & 0 & - 3 \\ - 1 & - 1 & 2 \end{matrix}]$ what is the associated eigenvalue?

Short Answer

Expert verified

Hence, the required eigenvalue is $位 = 2$

Step by step solution

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.

Finding eigenvalues

Consider $x = [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}]$ be an eigen vector of the matrix $[\begin{matrix} 4 & 1 & 1 \\ - 5 & 0 & - 3 \\ - 1 & - 1 & 2 \end{matrix}]$ .

The objective is to find the associated eigenvalue.

If xis an eigen vector of Athen $A x = 位 x$ where scalar $位$ is called an eigenvalue of A.

Consider,

$A x = 位 x [\begin{matrix} 4 & 1 & 1 \\ - 5 & 0 & - 3 \\ - 1 & - 1 & 2 \end{matrix}] [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}] = 位 [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}] [\begin{matrix} 4 & 1 & 1 \\ - 5 & 0 & - 3 \\ - 1 & - 1 & 2 \end{matrix}] = 位 [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}] [\begin{matrix} 2 \\ - 2 \\ - 2 \end{matrix}] = 位 [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}] 2 [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}] = 位 [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}]$

Hence, the associated eigen value is $位 = 2$

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91影视

We are told that $[\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}]$ is an eigenvector of the matrix $[\begin{matrix} 4 & 1 & 1 \\ - 5 & 0 & - 3 \\ - 1 & - 1 & 2 \end{matrix}]$ what is the associated eigenvalue?

Short Answer

Step by step solution

Definition of the Eigenvectors

Finding eigenvalues

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91影视

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

Short Answer

Step by step solution

Definition of the Eigenvectors

Finding eigenvalues

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

We are told that $[\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}]$ is an eigenvector of the matrix $[\begin{matrix} 4 & 1 & 1 \\ - 5 & 0 & - 3 \\ - 1 & - 1 & 2 \end{matrix}]$ what is the associated eigenvalue?