Question: Let H and K be subspaces of a vector space V. The intersection of H and K, written as H ( K, is the set

Let H and K be subspaces of a vector space V. The intersection of H and K, written as H ( K, is the set of v in V that belong to both H and K. Show that H ( K is a subspace of V. (See the figure.) Give an example in R2 to show that the union of two subspaces is not, in general, a subspace.

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