True/False: matrices and are said to be similar if for some invertible matrix .

Let such that and . Compute the following:

True/False: An matrix is diagonalizable if and only if has exactly eigenvectors.

Read the Diagonalization Theorem.

True/False: If a matrix has a linearly independent set of four eigenvectors, then is
diagonalizable.

Read the Diagonalization Theorem.

True/False: It is possible for an matrix to have a linearly independent set of more
than eigenvectors.

has eigenvalues (counting multiplicities). For each eigenvalue, the eigenspace has
dimension less than or equal to the multiplicity of the eigenvalue.