# Answer on Abstract Algebra Question 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.

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

2) Isn't even and isn't odd

3) one critical point, when3x+1=0, x=-1/3

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