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Given vector spaces V, W over a field, and linear transformation [itex]T:V\rightarrow W[/itex], prove [itex]T(0_{v})=0_{w} [/itex] where 0_v and 0_w are additive identities of V and W.
I'm trying to use the definition of additive identity. So, [itex]\forall\vec{v}\in V,\vec{v}+0=\vec{v+0=0} [/itex]. Where do I go from here?
I'm trying to use the definition of additive identity. So, [itex]\forall\vec{v}\in V,\vec{v}+0=\vec{v+0=0} [/itex]. Where do I go from here?