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Unformatted text preview: (5 pts.) Let U := { x R 3 : x 1 + 2 x 2x 3 = 0 } , and V := { x R 3 : x 12 x 2 + 2 x 3 = 0 } . Find a basis for ( i ) U, ( ii ) V, ( iii ) U V, ( iv ) span U V. Problem 4 (5 pts.) Recall a denition of scalar product on complex numbers. Let A = 3 1 1 2 . Prove that the product dened as u v := u T A v = 2 X i,j =1 u i a ij v j is a scalar product on C 2 , according to the denition. (At some point, it could be useful to remember that 2( ac ) a 2c 2 for all a,c R .)...
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 Spring '11
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