Exercise4

Provide a justification for your response to the following questions.

1. If $$A$$ is a $$3\times3$$ matrix having eigenvalues $$\lambda = 2, 3, -4\text{,}$$ can you guarantee that $$A$$ is diagonalizable?

2. If $$A$$ is a $$2\times 2$$ matrix with a complex eigenvalue, can you guarantee that $$A$$ is diagonalizable?

3. If $$A$$ is similar to the matrix $$B = \left[\begin{array}{rrr} -5 \amp 0 \amp 0 \\ 0 \amp -5 \amp 0 \\ 0 \amp 0 \amp 3 \\ \end{array}\right] \text{,}$$ is $$A$$ diagonalizable?

4. What matrices are similar to the identity matrix?

5. If $$A$$ is a diagonalizable $$2\times2$$ matrix with a single eigenvalue $$\lambda = 4\text{,}$$ what is $$A\text{?}$$

in-context