Explore BrainMass
Share

Explore BrainMass

    Linear Transformations, Rotations, Submodules and Subspaces

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

    (7) Let F=R, let V=R^2 and let T be the linear transformation from V to V which is rotation clockwise about the origin by pi-radians. Show that every subspace of V is an
    F[X]-submodule for this T.

    Here F[X] is a polynomial domain where the coefficient ring is a field F.

    © BrainMass Inc. brainmass.com October 9, 2019, 6:58 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/linear-transformations-rotations-submodules-and-subspaces-103616

    Solution Preview

    Proof:
    Here is a simple view for this problem.
    V=R^2 is a 2-dimensional space. If W is a subspace of V, then W is a line passing
    through the origin (0,0). T ...

    Solution Summary

    Linear Transformations, Rotations, Submodules and Subspaces are investigated.

    $2.19