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Miklós Schweitzer 2012 P5

Source: Miklós Schweitzer 2012 P5

August 20, 2018
college contests

Problem Statement

Let V1,V2,V3,V4V_1,V_2,V_3,V_4 be four dimensional linear subspaces in R8\mathbb{R}^8 such that the intersection of any two contains only the zero vector. Prove that there exists a linear four dimensional subspace WW in R8\mathbb{R}^8 such that all four vector spaces W∩ViW\cap V_i are two dimensional.
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