Problems of Eigenvectors and Eigenspaces. From introductory exercise problems to linear algebra exam problems from various universities. Basic to advanced level. From introductory exercise problems to linear algebra exam problems from various universities.
The dimension of the eigenspace corresponding to an eigenvalue is less than or equal to the multiplicity of that eigenvalue. The techniques used here are practical for $2 \times 2$ and $3 \times 3$ matrices.
For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue.