Find the Eigenvalues

Problem

det([[7,0,0,0,0],[1,3,0,0,0],[−2,7,0,0,0],[7,7,4,7,0],[8,8,−7,−9,3]]−λ*I)=0

Solution

1. Identify the type of matrix provided. The given matrix is a lower triangular matrix because all entries above the main diagonal are zero.

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

3. Extract the diagonal elements from the matrix. The elements on the main diagonal are 7 3 0 7 and 3

4. List the distinct eigenvalues and their algebraic multiplicities if necessary. The eigenvalues are λ=7 (multiplicity 2), λ=3 (multiplicity 2), and λ=0 (multiplicity 1).

Final Answer

λ={7,3,0,7,3}

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