Question: Problem 1. Let T : R > Rd be a linear transformation with standard matrix A. Prove that (a) The map T is surjective if

Problem 1. Let T : R\" > Rd be a linear transformation with standard matrix A. Prove that (a) The map T is surjective if and only if for all 5; 6 Rd, the system of linear equations An? = I; is consistent. (b) The map T is injective if and only if the system of linear equations A1? = 6 has a unique solution. _' _. (c) The map T is bijective if and only if for all b 6 Rd, the system of linear equations A13 : b has a unique solution

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