Suppose $W, U_1, U_2$ are subspaces from vector space $V$. If $W+U_1 =W + U_2$ then $U_1 = U_2$
If $W \cap U = \{0\}$ i can see it's correct. But here it only talks about sum. So can you provide a counterexample for this?
2026-03-25 15:10:43.1774451443
Linear Algebra: Is this proposition correct?
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Sure. Here's a very general conterexample: take $U_1$ and $U_2$ as distinct subspaces of $W$. Then $W+U_1=W+U_2=W$, but $U_1\neq U_2$.