Find the Eigenvalues

Problem

[[1,3,2,11],[0,−1,3,8],[0,0,−2,4],[0,0,0,2]]

Solution

1. Identify the type of matrix provided. The given matrix 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. Extract the diagonal entries from the matrix. The entries on the main diagonal are 1 −1 −2 and 2

4. List the eigenvalues. These values represent the roots of the characteristic equation det(A−λ*I)=0

Final Answer

λ=1,−1,−2,2

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