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Unformatted text preview: Tutorial VAM: Vector Algebra and an Introduction to Matrices = ( ijk jnp ) lmi a l b m c n d p = ( ip kn in kp ) lmi a l b m c n d p = lmi a l b m ( c k d i c i d k ) = ( A B ) i ( c k d i c i d k ) = [ ( A B ) D ] c k [( A B ) C ] d k : Exercise 19. If A ; B and C are not linearly independent, then they can be related as in Eqn. 41: 1 A + 2 B + 3 C = ; for non-zero i : Taking the scalar product of this equation by each of the vectors in turn gives the set of three equations, 1 A A + 2 A B + 3 A C = ; ; 1 B A + 2 B B + 3 B C = ; ; 1 C A + 2 C B + 3 C C = ; : These equations can be solved to give the i in terms of each other, up to a common factor, in terms of the scalar products. Exercise 20. Applying the previous procedure to the vectors ^ x ; ^y and ^z and using Eqn. 26 yields 1 1+ 2 0 + 3 = 0= ) 1 = 0 ; 1 0+ 2 1 + 3 = 0= )...
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This note was uploaded on 07/13/2008 for the course PHY 201 taught by Professor Covatto during the Spring '08 term at ASU.
- Spring '08