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1C p16

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Signed-off-by: szdytom <szdytom@qq.com>
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@ -428,3 +428,13 @@
][ ][
由子空间加法封闭性可知，$U + U = U$。 由子空间加法封闭性可知，$U + U = U$。
] ]
#exercise_sol(type: "proof")[
$V$ 的“子空间求和”运算可交换吗？换句话说，设 $U$ 和 $W$ 都是 $V$ 的子空间，那么 $U + W = W + U$ 是否成立？
][
是的。我们有
$ U + W = {u + w : u in U, w in W} = {w + u : u in U, w in W} = W + U $
#tab 这说明 $U + W = W + U$ 成立。
]