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Unformatted text preview: R W P 6 ! P 7 . (c) Observe that multiplication by 1 C 3x C 2x 2 is linear from P 5 to P 7 , and nd the matrix of this linear map. 3.4.11. Let B D .v 1 ;:::;v n / be an ordered basis of a vector space V over a eld K . Denote the dual basis of V by B D v 1 ;:::;v n . Show that for any v 2 V and f 2 V , h v;f i D n X j D 1 h v;v j ih v j ;f i : 3.4.12. Let B D .v 1 ;:::;v n / and C D .w 1 ;:::;w n / be two bases of a vector space V over a eld K . Denote the dual bases of V by B D v 1 ;:::;v n and C D w 1 ;:::;w n . Recall that id B;C is the matrix with .i;j/ entry equal to h w j ;v i i , and similarly, id C;B is the matrix with .i;j/ entry equal to h v j ;w i i . Use the previous exercise to show that id B;C and id C;B are inverse matrices....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

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