Find the Eigenvalues

Problem

[[5,−3,0,2],[0,2,4,−1],[0,0,2,3],[0,0,0,5]]

Solution

1. Identify the type of matrix. The given matrix A is an upper triangular matrix because all entries below the main diagonal are zero.

2. Apply the property of triangular matrices. For any upper or lower triangular matrix, the eigenvalues are exactly the entries located on the main diagonal.

3. List the diagonal elements. The entries on the main diagonal of the matrix are 5 2 2 and 5

4. Determine the unique eigenvalues. The distinct values from the diagonal are 2 and 5 each appearing with an algebraic multiplicity of 2

Final Answer

Eigenvalues=2,5

Want more problems? Check here!