We have a three dimensional vector space where |P1), |P2) and |23) form a completeorthonormal basis.In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|.ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".

We have a three dimensional vector space where |P1), |P2) and 43) form a complete orthonormal basis. In this vector space we have two states |a)=5i|P1)+3i|42)+(-2+2i)|P3) and |B) =4i|4 1)-5 |92)+l93) i) Calculate (a| and (B|, in terms of the dual basis vectors (1|, (42|, (23)- ii) Calculate the inner/scalar products (@|B) and (B|a). Show that (B|a) =(a|B)".

We have a three dimensional vector space where |P1), |P2) and 43) form a complete orthonormal basis. In this vector space we have two states |a)=5i|P1)+3i|42)+(-2+2i)|P3) and |B) =4i|4 1)-5 |92)+l93) i) Calculate (a| and (B|, in terms of the dual basis vectors (1|, (42|, (23)- ii) Calculate the inner/scalar products (@|B) and (B|a). Show that (B|a) =(a|B)".

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