# Solution: 2016-20 Finding a subspace

Let $$V_1,V_2,\ldots$$ be countably many $$k$$-dimensional subspaces of $$\mathbb{R}^n$$. Prove that there exists an $$(n-k)$$-dimensional subspace $$W$$ of $$\mathbb{R}^n$$ such that $$\dim V_i\cap W=0$$ for all $$i$$.

The best solution was submitted by Shin, Joonhyung (신준형, 수리과학과 2015학번). Congratulations!

Here is his solution of problem 2016-20.

Alternative solutions were submitted by 김태균 (2016학번, +3), 국윤범 (수리과학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3, alternative solution). One incorrect solution was submitted.

GD Star Rating