For thesquase matrixA1.1-ノdetermine the Characteristic Eguationfor the Eien Values ef Giventhat A= -3 is anEigen Valueof A; usc polynmial-tong divisionto determine the remainingEigen Valnces at A.Determine theEigen Vector corresponding to thelarguest Eigen Value atEigen Valuie of A.

Answered: or A 1. 1- determine the Characteristic…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

For the
squase matrix
A
1.
1-
ノ
determine the Characteristic Eguation
for the Eien Values ef Given
that A= -3 is an
Eigen Value
of A; usc polynmial-tong division
to determine the remaining
Eigen Valnces at A.Determine the
Eigen Vector corresponding to the
larguest Eigen Value at
Eigen Valuie of A.

Expert Solution

Step 1

To find the characteristic equation,

$|\begin{matrix} 2 - λ & 1 & 2 \\ - 1 & 1 - λ & - 1 \\ 8 & 3 & 0 - λ \end{matrix}| = 0 (2 - λ) [(1 - λ) (0 - λ) - (- 1) (3)] - 1 [(- 1) (- λ) - (- 1) 8] + 2 [(- 1) 3 - (1 - λ) (8)] = 0 λ^{3} - 3 λ^{2} - 10 λ + 24 = 0$

As given that $λ = - 3$ that $λ + 3$ is a factor for the characteristic equation.

Therefore, the final characteristic equation will be:

$(λ + 3) (λ - 2) (λ - 4) = 0$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions