True or false: If A {\displaystyle A} is invertible, then A {\displaystyle A} is diagonalizable.
lim x → ∞ 3 − 2 x 2 5 x 2 + x + 1 = L ′ H lim x → ∞ − 4 x 10 x + 1 = L ′ H − 4 10 = − 2 5 . {\displaystyle {\begin{array}{rcl}\displaystyle {\lim _{x\rightarrow \infty }{\frac {3-2x^{2}}{5x^{2}+x+1}}}&{\overset {L'H}{=}}&\displaystyle {\lim _{x\rightarrow \infty }{\frac {-4x}{10x+1}}}\\&&\\&{\overset {L'H}{=}}&\displaystyle {\frac {-4}{10}}\\&&\\&=&\displaystyle {-{\frac {2}{5}}}.\end{array}}}
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is invertible, then is diagonalizable.
so that we can use L'Hopital's rule.
