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Let $L\colon M_{2 \times 3} \to M_{3 \times 3}$ be the linear transformation defined by $L(A) = \left[\begin{array}{rr}2 & -1 \\ 1 & 2 \\ 3 & 1\end{array}\right]\,A$. Find the dimension of the range of $L$.

Answer: $6$

How is the answer $6$? Isn't it $2$?

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    I assumed that "M23" was the space of $2 \times 3$ matrices. It would not hurt to make this explicit, nor would it hurt to learn $\TeX$!2012-06-20
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    Welcome to math.SE! In order to get better answers, you could explain a bit what you've tried, and what you know. For example, why do you think its rank is $2$?2012-06-21

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