-1
$\begingroup$

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 ?

  • 2
    If not, the dimension formula is $\dim(S+T)=\dim(S)+\dim(T)-\dim(S\cap T)$. It'll help to think about the case when $T\subset S$ as well as the case when $S$ and $T$ jointly span $\mathbb{R}^{24}$.2012-09-30
  • 0
    ok sir!! I am trying to solve it.2012-09-30
  • 1
    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