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Linear Transformations, Rotations, Submodules and Subspaces

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(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.

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Solution Preview

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.