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## Main Question or Discussion Point

How to prove that the dim of two subspaces added together equals dim of their union plus 1 iff one space is a subest of the other

In other words,

subspaces: V, S of Vector space: W

[tex] dim(V+S) = dim(V \cap S) +1 [/tex]

if [tex]V \subseteq S[/tex] or [tex]S \subseteq V [/tex]

In other words,

subspaces: V, S of Vector space: W

[tex] dim(V+S) = dim(V \cap S) +1 [/tex]

if [tex]V \subseteq S[/tex] or [tex]S \subseteq V [/tex]