what does it mean, when you say T is in the linear transformation from V to W??

is T a vector? or is T something else?

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- Nov 12th 2008, 05:38 AM #1

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- Nov 12th 2008, 05:57 AM #2

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- Nov 12th 2008, 07:02 AM #3

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## thanks just one more thing

i know that the range of T in T:V to W is = Tv: (v in V)

and for some tranformation to be surjective, the Range of T has to equal to W, but shouldn't all RangeT should be equal to W??

could I get some examples of a surjective transformation and an explanation on why??

thank you

- Nov 12th 2008, 08:15 AM #4
Consider the mapping $\displaystyle T:R^3 \mapsto R^2 \,,\,T\left[ \begin{gathered}

a \hfill \\ b \hfill \\ c \hfill \\ \end{gathered} \right] = \left[ \begin{gathered}

a + b \hfill \\ c - b \hfill \\ \end{gathered} \right]$

In that a linear mapping?

If $\displaystyle \left[ \begin{gathered} x \hfill \\ y \hfill \\ \end{gathered} \right] \in R^2 \,\& \,T\left[ \begin{gathered} x \hfill \\ 0 \hfill \\ y \hfill \\ \end{gathered} \right] = ?$.

What does that tell you about surjectivity?