# Linear Algebra : Subspaces

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a. Let U and V be subspaces of R^n. Define the intersection of U and V to be

U n V = {x E R^n : x E U and x E V}.

Show that U n V is a subspace of R^n. Give two examples.

b. Is U u V = {x E R^n : x E U or x E V} a subspace of R^n? Give a proof or counterexample.

(Above n represents the union sign and E the belonging to symbol)

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(The material is from Subspace of Rn. Please show each step of your solution. Thank you.)

Proof.

a) To prove that is a subspace of , we need to ...

#### Solution Summary

The subspaces in question are investigated. The solution is detailed and well presented.

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