Properties of eigenvectors and eigenvalues

Find the algebraic and geometric multiplicity of each eigenvalue of the following matrices. Which of the matrices are diagonalizable?

Determine which of the following matrices are diagonalizable.

1. $A$ is a $3\times 3$-matrix with eigenvalues $-1$ and $3$. The eigenvalue $-1$ has algebraic multiplicity $2$ and geometric multiplicity $1$. The eigenvalue $3$ has algebraic and geometric multiplicity $1$.

2. $B$ is a $4\times 4$-matrix with eigenvalues $2$ and $-2$. The eigenvalue $2$ has algebraic and geometric multiplicity $1$. The eigenvalue $-2$ has algebraic and geometric multipl…