a. A linear transformation is a special type of function. A. True. A linear transformation is a function from R to R that assigns to each vector x in IR a vector T(x) in R. B. True. A linear transformation is a function from R" to Rm that assigns to each vector x in R^ a vector T(x) in Rm. OC. False. A linear transformation is not a function because it maps more than one vector x to the same vector T(x). D. False. A linear transformation is not a function because it maps one vector x to more than one vector T(x). b. If A is a 3×5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R³. A. True. The domain is R³ because A has 3 columns, because in the product Ax, if A is an mxn matrix then x must be a vector in RM B. False. The domain is actually R5, because in the product Ax, if A is an mxn matrix then x must be a vector in R". C. False. The domain is actually R, because in the product Ax, if A is an mxn matrix then x must be a vector in R. D. True. The domain is R³ because A has 3 rows, because in the product Ax, if A is an mxn matrix then x must be a vector in Rm. c. If A is an mxn matrix, then the range of the transformation x → Ax is Rm. A. True. The range of the transformation is RM, because each vector in R is a linear combination of the rows of A. B. False. The range of the transformation is the set of all linear combinations of the columns of A, because each image of the transformation is of the form Ax. C. True. The range of the transformation is RM, because each vector in R is a linear combination of the columns of A. D. False. The range of the transformation is R" because the domain of the transformation is RM