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 deﬁnition of scalar product on complex numbers. Let A = ± 3 1 1 2 ² . Prove that the product deﬁned 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 deﬁnition. (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
 N/A
 Linear Algebra, Vector Space, scalar product, ui aij vj

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