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# Let $V$ and $W$ be vector spaces over a field $mathbb{F}$. Show that a map $T: V ightarrow W$ is linear if and only if$$Tleft(a v_{1}+v_{2}ight)=a T v_{1}+T v_{2}$$...

## Question

###### Let $V$ and $W$ be vector spaces over a field $mathbb{F}$. Show that a map $T: V ightarrow W$ is linear if and only if$$Tleft(a v_{1}+v_{2}ight)=a T v_{1}+T v_{2}$$for any $oldsymbol{v}_{1}, oldsymbol{v}_{2} in V$ and $a in mathbb{F}$

Let $V$ and $W$ be vector spaces over a field $mathbb{F}$. Show that a map $T: V ightarrow W$ is linear if and only if $$Tleft(a v_{1}+v_{2} ight)=a T v_{1}+T v_{2}$$ for any $oldsymbol{v}_{1}, oldsymbol{v}_{2} in V$ and $a in mathbb{F}$ #### Similar Solved Questions

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