A9S - ASSIGNMENT 9 Solutions Let U1 and U2 be the following...

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ASSIGNMENT 9 Solutions Let U 1 and U 2 be the following hyperplanes: U 1 = x 1 x 2 x 3 x 4 : 2 x 1 + x 2 - 2 x 4 = 0 , U 2 = x 1 x 2 x 3 x 4 : x 1 + x 2 + x 3 + x 4 = 0 . 1. [4 marks] Find hyperplanes V 1 and V 2 such that ( U 1 U 2 ) = V 1 V 2 . Note that U 1 = Nul ± 2 1 0 - 2 ² and U 2 = Nul ± 1 1 1 1 ² ; that is, U 1 U 2 = Nul ³ 2 1 0 - 2 1 1 1 1 ´ . Let A denote the 2 × 4 matrix above. Now (Nul A ) = Row A . It remains to find hyperplanes V 1 and V 2 such that V 1 V 2 = Row A . It may be shown that Nul A has a basis 1 - 2 1 0 , 3 - 4 0 1 . Hence V 1 = x 1 x 2 x 3 x 4 : x 1 - 2 x 2 + x 3 = 0 and V 2 = x
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A9S - ASSIGNMENT 9 Solutions Let U1 and U2 be the following...

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