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Consider the set of all functions that can be written in the form A­ sin (t + θ ). This set can…

Consider the set of all functions that can be written in the form A­ sin (t + θ ). This set can…

Consider the set of all functions that can be written in the form A­ sin (t + θ). This set can be considered a vector space, because it satisfies the ten defining properties.i. Consider the following basis set for the vector space described above:  Represent the vector  as a column of numbers xv (find the vector expansion), using this basis set.ii. Using your basis set from part i., find vector expansions foriii. We now want to represent the vector  of part i., using the basis set   Use reciprocal basis vectors to find the expansion for in terms of the basis vectors  This will allow you to write   as a new column of numbers xu.iv. Show that the representations for  hat you found in parts i. and iii. are equivalent (the two columns of numbers  both represent the same vector )