1. Let T: C² C² be defined by T((x, y)) = (x + y, iy). (a.) Show that T is a linear transformation over R. (b.) Find matrix representation T relative to the standard basis. (c.) Give a non-standard basis, 3 for vector space C² over R. Then, find matrix representation T relative to 3. (d.) Determine whether there is a relation between matrix representations in (b.) and (c.). Justify your answer.

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