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Math_260 Test3

QuestionAnswer
*onto A mapping T R^n—R^m such taht each b in R^m is the image of AT LEAST one x in R^n.
* one-to-one(mapping) A mapping T R^n—R^m such taht each b in R^m is the image of AT MOST one x in R^n.
*transpose An n x m matrix A^T whose columns are the corresponding rows of the m x n matrix A
*equal matrices An invertible matrix that results by performing one elementary row operation on an identity matrix.
*transformation, function, mapping A rule that assigns to each vector x in R^n a unique vector T(x) in R^m.
*domain The set of all vectors x for which T(x) is defined.
* codomain the set of R^m that contains the range of T. In general if T maps a vector space V into a vector space W, then W is called the codomain of T
* range the set of all vectors of the form T(x) for some x in the domain of T.
*image, preimage The vector T(x) assigned to x by T.
*linear transformation T (from a vector space V into a vector space W) A rule T that assigns to each vector x in V a unique vector T(x) in W, such that (i)T(u+v)=T(u)+T(v) for all u, v in V, and (ii) T(cu)=cT(u) for all u in V and all scalars C.
Created by: slonczt