Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 17E from Chapter 5.2 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 17E
Chapter:
Problem:
For the matrices in Exercises 15–17, list the real eigenvalues, repeated according to their multiplicities.
Step-by-Step Solution
Given Information
We are given with a matrix\[A = \left[ {\begin{array}{*{20}{r}}3&0&0&0&0\\{ - 5}&1&0&0&0\\3&8&0&0&0\\0&{ - 7}&2&1&0\\{ - 4}&1&9&{ - 2}&3\end{array}} \right]\]We have to list the eigenvalues, repeated according to their multiplicities.
Step-1: Eigenvalues
We can see that given matrix is a lower triangular matrix, so eigenvalues are given by the diagonal entries of the matrix, so First eigenvalue is 0, Second eigenvalue is 1 with multiplicity 2, and third one is 3 with multiplicity 2; \[\lambda = 3,1,0,1,3\]
We are given with a matrix\[A = \left[ {\begin{array}{*{20}{r}}3&0&0&0&0\\{ - 5}&1&0&0&0\\3&8&0&0&0\\0&{ - 7}&2&1&0\\{ - 4}&1&9&{ - 2}&3\end{array}} \right]\]We have to list the eigenvalues, repeated according to their multiplicities.
Step-1: Eigenvalues
We can see that given matrix is a lower triangular matrix, so eigenvalues are given by the diagonal entries of the matrix, so First eigenvalue is 0, Second eigenvalue is 1 with multiplicity 2, and third one is 3 with multiplicity 2; \[\lambda = 3,1,0,1,3\]