 # 2. Provide an example of a 3x3 matrix with two eigenvalues λ...

## Question

2. Provide an example of a 3x3 matrix with two eigenvalues λ1 = 1, with algebraic multiplicity = 2 and geometric multiplicity = 2, and λ2 = 3. Find the eigenvectors associated with each eigenvalue.
3. Provide an example of a 3 X 3 matrix with two eigenvalues λ1 = 1, with algebraic multiplicity = 2 and geometric multiplicity = 1, and λ2 = 3. Find the eigenvectors associated with each eigenvalue.
4. Provide an example of a 3 X 3 matrix with one eigenvalue λ1 = 1, with algebraic multiplicity = 3 and geometric multiplicity = 2. Find the eigenvectors associated with the eigenvalue.
5. Provide an example of a 3 X 3 matrix with three eigenvalues λ1 = 1, λ2 = 2, and λ3 = 3. Find the eigenvectors associated with these eigenvalues.

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