Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Suppose we select $(n-k)$ linearly independent vectors from set $\mathcal{I}$. Is there a way to show that the vector space formed by these vectors satisfies this property using induction on the size of the smallest vector space in $\mathcal{I}$ ?
