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Answer to Question #17769 in Abstract Algebra for Ciaran Duffy

Question #17769
(i) For non-trivial subspaces U and W of a (finite-dimensional) vector space V, define
U +W := {u + w | u element of U and w element of W}.
Prove that U +W is a subspace of V .
(ii) Show that
dim(U +W) = dim(U) + dim(W) − dim(U intersect W)
by considering a basis for U intersect W, extending it to bases for U and W, and then
identifying, with justification, a basis for U +W in terms of these elements.
Expert's answer
1) domain: (-inf,inf)/{0}
2) Isn't even and isn't odd
3) one critical point, when3x+1=0, x=-1/3

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