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Linear Algebra With Applications
Found in: Page 336
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

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.


Eigenvalues are:


See the step by step solution

Step by Step Solution

Step 1: Eigenvalues

  • In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by λ , is the factor by which the eigenvector is scaled.
  • Eigenvalues of a triangular matrix are its diagonal matrix.

Step 2: Finding all real eigenvalues, with their algebraic multiplicities

Since, given matrix is triangular its eigenvalues are the entries on the main diagonal.

Find eigenvalues using characteristic equation as:



Hence, the answer is:


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