TRUE OR FALSE?
38. There exists a subspace of that is isomorphic to.
The given statement is true.
Two vector spaces V and W over the same field F are isomorphic if there is a bisection which preserves addition and scalar multiplication, that is, for all vectors u and v in V, and all scalars .The correspondence T is called an isomorphism of vector spaces.
When is an isomorphism, then it’s emphasize that it is an isomorphism When V and W, are isomorphic, but the specific isomorphism is not named, we’ll just write .
Space is 12-dimensional and is 10-dimensional. Spaces of same dimension are isomorphic, so any 10-dimensional subspace of is isomorphic to .
Hence, the statement is true.
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