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Consider the vectors defined in Figure E15.6. The set is the standard basis set. The set is an…

Consider the vectors defined in Figure E15.6. The set is the standard basis set. The set is an…

Consider the vectors defined in Figure E15.6. The set  is the standard basis set. The set  is an alternate basis set. The vector  is a vector that we wish to represent with respect to the two basis setsi. Write the expansion for  in terms of the standard basis ii. Write the expansions for u1 and u2 in terms of the standard basis iii. Using reciprocal basis vectors, write the expansion for  in terms of the basis iv. Draw sketches, similar to Figure 5.2, that demonstrate that the expansions of part i. and part iii. are equivalent.