Explore BrainMass

Explore BrainMass

    Vector 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!

    Suppose that V and W are vector subspaces of Rn. If I define:

    V + W = {v+w: v belonging to V, w belonging to W}

    How can I prove that V+W is also a vector subspace of Rn and ALSO how could verify that (for example)
    <(1,0,1), (-1,0,1)> + <(3,2,1)> = R3

    Thanks

    © BrainMass Inc. brainmass.com June 7, 2023, 2:47 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/vector-subspaces-defined-24521

    Solution Preview

    See attachment

    Follow up from OTA on Student Comment:
    To answer your questions in the comment:

    Yes, it works with any square matrix.

    I have in my old algebra text a theorem (Elementary Linear Algebra with Applications by W. Keith Nicholson):
    The ...

    Solution Summary

    Vector subspaces are investigated. The solution is detailed and well presented.

    $2.49

    Free BrainMass Quizzes

    • Multiplying Complex Numbers

      This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

    • Graphs and Functions

      This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

    • Solving quadratic inequalities

      This quiz test you on how well you are familiar with solving quadratic inequalities.

    • Probability Quiz

      Some questions on probability

    • Know Your Linear Equations

      Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

    View More Free Quizzes