Show by a counter-example that if U+W =U+X for subspaces U,W,X of V, then W need not be equal to X.
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Standard one: $U:=\text{span};(1,0)$, the x axis, $W:=\text{span};(1,1)$, $X:=\text{span};(0,1)$, the y axis and $V:=\Bbb R^2$ – Chinnapparaj R Sep 14 '19 at 08:20
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Sep 14 '19 at 08:22