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TIFR-2018-Maths-A-15True/False Question :

The set of nilpotent matrices in $M_{3}\left ( \mathbb{R} \right )$ spans $M_{3}\left ( \mathbb{R} \right )$ considered as an $\mathbb{R}$-vector space (a matrix $A$ is said to be nilpotent if there exists $n \in \mathbb{N}$ such that $A^{n}=0$).

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