031 Review Problems

This is a list of sample problems and is meant to represent the material usually covered in Math 31. An actual test may or may not be similar.

1. True or false: If all the entries of a $7\times 7$ matrix $A$ are $7,$ then det $A$ must be $7^{7}.$

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2. True or false: If a matrix $A^{2}$ is diagonalizable, then the matrix $A$ must be diagonalizable as well.

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3. True or false: If $A$ is a $4\times 4$ matrix with characteristic equation $\lambda (\lambda -1)(\lambda +1)(\lambda +e)=0,$ then $A$ is diagonalizable.

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4. True or false: If $A$ is invertible, then $A$ is diagonalizable.

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