Suppose UUU and WWW are both five-dimensional subspaces of R9\mathbf R^9R9. Prove U∩W≠{0}U \cap W \ne \{0\}U∩W={0}
By 2.43
Since dimU∩W≥1\dim U\cap W \ge 1dimU∩W≥1 we must have U∩W≠{0}U \cap W \ne \{0\}U∩W={0}.