031 Review Part 1, Problem 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.

Solution:
The eigenvalues of  $A$  are  $0,1,-1,-e.$
Hence, the eigenvalues of  $A$ are distinct.
Therefore,  $A$  is diagonalizable and the statement is true.

Final Answer:
TRUE

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