3
$\begingroup$

Let $A$ be a $2\times2$ real square matrix of rank $1$. If $A$ is not diagonalizable, then which of the following is true.
(a) $A$ is nilpotent
(b) $A$ is not nilpotent
(c) the characteristic polynomial of $A$ is linear.
(d) $A$ has a non-zero eigenvalue.

I can say that d is false.

  • 0
    Given the context that you have stated, you should not think of trying to brute force the coordinates. Instead, think about what facts you know, and how to apply them to solve this problem.2012-12-30

4 Answers 4