Find the eigenvalues of a 3x3 matrix.

Published on December 1, 2024

Linear-Algebra

The eigenvalues of the given 3x3 matrix are 1, 2, and 2.

Question

Answer

Here’s how to find the eigenvalues of the given matrix:

The matrix is given by:

To find the eigenvalues, we need to solve the characteristic equation, which is given by:

where

represents the eigenvalues and

is the identity matrix.

So, we have:

Calculating the determinant, we get:

This gives us the eigenvalues:

So, the eigenvalues are 2 (with multiplicity 2) and 1.

Final Answer: The final answer is

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