Explore BrainMass

Explore BrainMass

    Linear Algebra : Subspaces

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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)

    © BrainMass Inc. brainmass.com March 4, 2021, 8:24 pm ad1c9bdddf

    Solution Preview

    Please see the attached file for the complete solution.

    Thanks for using BrainMass.

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


    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.