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Linear Algebra : Subspaces

Please show each step of your solution.

Thank you.

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)

Solution Summary

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