Question: consider two planes. P1 and P2 through the origin in R3, Show that there is a vector uR^3 with u 0 such that the vector

consider two planes. P1 and P2 through the origin in R3, Show that there is a vector uR^3 with u 0 such that the vector u is in both planes. This result may seem intuitive to you, but here we are asking you to use our linear alegbra techniques to show this, A proof by picture is not accepted.

b) Consider the matrices A and B, which are two 3 x 3 matrices of rank equal to one. Show that there is a vector v R^3 with v 0 such that both

Av = 0 and Bv = 0. you may use the results from part (a) if you find it helpful.

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