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Unformatted text preview: x 1 + x 2 + x 3 = 3 x 3 = 1 x 1 + x 3 = 2 2 x 1 + 5 x 3 = 87 x 1 + 8 x 2 = 0 x 1 + 2 x 2x 3 = 1 . 6. Find the minimum norm solution of the system 2 x 1 + x 2 + x 3 + 5 x 4 = 8x 1x 2 + 3 x 3 + 2 x 4 = 0 . 7. Let A be a matrix with linearly independent columns, and let M = R ( A ). Prove the following: (a) AA A = A (b) A A = ( A A ) (c) P M is symmetric. (d) P M 2 = P M ....
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 Spring '12
 DouglasWard
 Math

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