Explore BrainMass

Explore BrainMass

    Linear Algebra - Four Fundamental 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!

    (The material is from the Four Fundamental Subspaces. Please show each step of your solution. )

    Theorem 4.7:

    Let A be an m x n matrix. Then

    1. R (A) ┴ = N (A)
    2. N (A) ┴ = R (A)
    3. C (A) ┴ = N (A┬)
    4. N (A┬) ┴ = C (A)

    © BrainMass Inc. brainmass.com March 4, 2021, 8:32 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/linear-algebra-four-fundamental-subspaces-175054

    Attachments

    Solution Preview

    Please see the attachment.

    Proof:
    (a) For any , we have , then .
    On the other hand, if , then .
    We note that is actually a linear ...

    Solution Summary

    This solution is comprised of a detailed explanation to answer Linear Algebra - Four Fundamental Subspaces.

    $2.49

    ADVERTISEMENT