Question: Let V be a vector space of dimension n, and let W, W2 be subspaces of V. (a) Assume that W W = {0}.

Let V be a vector space of dimension n, and let W,

Let V be a vector space of dimension n, and let W, W2 be subspaces of V. (a) Assume that W W = {0}. Show that dim(W W) = dim(W) + dim(W). ( where the direct sum W W of two subspaces W and W of a vector space V is defined). (b) Assume that dim(W) + dim(W) = n. Does it follow that W + W = V? Justify your answer by either proving the equality or providing an example where it does not hold.

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a To show that dimW W dimW dimW when W W 0 we can use the ranknullity theorem By definition W W is t... View full answer

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