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8. (9 points) (a) Consider two planes, P1 and P2, through the origin in R3. Show that there is a vector u e R3 with u / 0 such that u is in both planes. This result may seem intuitive to you, but here we are asking you to use our linear algebra techniques to show this. A proof by picture will not be accepted. (b) Consider the matrices A and B, which are two 3 x 3 matrices of rank equal to 1. Show that there is a vector 7 E R3 with v / 0 such that both AU = 0 and BU = 0. You may use the result from part (a) if you find it helpful, whether or not you were able to show it. I Recall that planes through the origin in R' are two-dimensional subspaces, given by the solutions of a non-zero linear homogeneous equation, or given by all vectors perpendicular to some non-zero vector that we call the normal vector. You may use any of these facts without proving them