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Vector Subspace of Vector Spaces

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1. Determine whether the following sets W are vector subspaces of the
vector space V.
a. V=R^4, A and B are two 3 X 4 matrices.
W={X is an element of R^4:Ax-3Bx=0}.
b. V=C', W={f is an element of C': f(x+3)=f(x)+5
c. V=P, W={f is an element of P: f'(2)=0}
d. V=C', W={f is an element of C': The integral of f(x)dx from 0 to
3 = 2f(3)

I understand how to verify a vector subspace of a vector space, if it is closed under addition and scaler multiplication. I am having trouble understanding and handling the notation. Not sure which way to go.

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Solution Summary

This shows how to determine if sets are vector subspaces of the given vector space. The element functions are examined.

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