Find the Eigenvalues [[0,1],[0,0]]

Problem

[[0,1],[0,0]]

Solution

1. Identify the matrix A and the characteristic equation formula det(A−λ*I)=0 where I is the identity matrix and λ represents the eigenvalues.

2. Set up the characteristic matrix by subtracting λ from the diagonal elements of the given matrix.

A−λ*I=[[0−λ,1],[0,0−λ]]=[[−λ,1],[0,−λ]]

3. Calculate the determinant of the characteristic matrix and set it equal to zero.

det(−λ)=(−λ)*(−λ)−(1)*(0)

4. Simplify the resulting characteristic polynomial.

λ2=0

5. Solve for λ to find the eigenvalues.

λ=0

Final Answer

λ=0

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