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Linear Algebra

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Diagonalize Parameterized Matrix

LINALG-E3IXE5

Let:

$$A_t=\begin{pmatrix} 1 & 0 & 0\\\ 0 & 1 &-1\\\ t^2 & t & 1\end{pmatrix}$$

...where $t\in\mathbb{R}$.

For which values of $t$ is $A_t$ diagonalizable over $\mathbb{R}$?

A

$t\in [-1,1]$ only

B

$t<0$

C

$t\geq 0$

D

For all $t\in\mathbb{R}$