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Linear Algebra

Exercise 2.1.17

Answers

1.: Because rank $(T) \leq$ dim $(V) <$ dim $(W)$ by Dimension Theorem, we have $R (T) ⊊ W$ .
2.: Because nullity $(T) =$ dim $(V) -$ rank $(T) \geq$ dim $(V) -$ dim $(W) > 0$ by Dimension Theorem, we have $N (T) \neq {0}$ .

jephianlin

2011-06-27 00:00

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