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Linear Algebra

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Symmetric and Diagonalizable

LINALG-JQ5IG2

If $A=\begin{pmatrix} e & f \\\ f & g\end{pmatrix}$ where $e,f,g$ are real numbers then:

A

$A$ is diagonalizable if $e\neq g$

B

$A$ is diagonalizable only if $f=0$

C

$A$ is diagonalizable only if $eg-f^2\neq 0$

D

$A$ is diagonalizable only if $e=g$