Find the Eigenvalues

Problem

[[3,−4,0,6],[0,2,3,−7],[0,0,6,8],[0,0,0,3]]

Solution

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

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

3. Extract the diagonal entries. The entries on the main diagonal of the matrix are 3 2 6 and 3

4. List the eigenvalues. The eigenvalues λ are the values found on the diagonal, noting that 3 has a multiplicity of 2

Final Answer

λ=3,2,6,3

Want more problems? Check here!