Final answer:
To find eigenvectors by inspection, follow these steps: find the eigenvalues of the matrix, substitute each eigenvalue back into the matrix and solve the equation, and the solutions will be the eigenvectors.
Step-by-step explanation:
To find eigenvectors by inspection, we can use the following steps:
- Start by finding the eigenvalues of the matrix.
- For each eigenvalue, substitute it back into the matrix and solve the equation (A - λI)x = 0, where A is the matrix, λ is the eigenvalue, and I is the identity matrix.
- The solutions to this equation will be the eigenvectors corresponding to each eigenvalue.