I am working on an example of vector spaces. I have the following question:
Let $\{V_1,V_2,\ldots,V_t\}$ be a family of $n$-dimensional subspaces and the dimension intersection of any $n$ subspace is at least one. Is it true that
$\dim \bigcap^{i=t}_{i=1}V_i\geq1$?
I have calculated $\dim \bigcap^{i=t}_{i=1}V_i$ for several spaces and all of spaces satisfied in $\dim \bigcap^{i=t}_{i=1}V_i\geq1$.
Can anybody take counterexample?