I have E, F, G as subspaces of V.
Confused as to how to start proving that if E + F = E + G, then F = G. Also the same except with direct sum. Assuming it involves evaluating combined summation but not sure.
2026-03-25 07:42:10.1774424530
summation properties of three subspaces?
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False for $V\neq\{0\}$. Let $G=\{0\}$, and $v\in V\setminus\{0\}$. Let $E=F=\langle v\rangle$. Then $E+F=E+G$.