Problem 1 (30 points) Which of the following mappings is a linear transformation 7 Use the definition of a linear transformation to justify your answer in each case. a) : R = R3 given by the rule (z;, s, x3) = (z3 + 23, 21; + 23,37) T3 + T3) b) : R? R? given by the rule (zy, x3, z3) (221 + z9, 13) c) : M5(C) C given by the rule A det(A)