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let $S$ and $T$ be two subspaces of $R^{24}$, such that $\dim(S)= 19$ and $\dim(T)= 17$, then the

a. Smallest possible value of $\dim(S \cap T)$ is ?

b. largest possible value of $\dim(S \cap T)$ is ?

c. Smallest possible value of $\dim(S + T)$ is ?

d. largest possible value of $\dim (S + T)$ is ?

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    I changed $dim(S)$ to $\dim(S)$, coded as \dim(S). These doesn't only prevent italicization, but also results in proper spacing in things like $a\dim B$.2012-09-30

1 Answers 1

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Hints:

$(1)\;\;\;\;\;\;\dim(S+T)=\dim S+\dim T-\dim(S\cap T)$

$(2)\;\;\;\;\;\;\forall\;\; K\leq \Bbb R^{24}\,\,,\,\,0\leq\dim K\leq \dim\Bbb R^{24}=24$