Math_260 Test3
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| *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.
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| * 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.
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| *transpose | An n x m matrix A^T whose columns are the corresponding rows of the m x n matrix A
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| *equal matrices | An invertible matrix that results by performing one elementary row operation on an identity matrix.
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| *transformation, function, mapping | A rule that assigns to each vector x in R^n a unique vector T(x) in R^m.
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| *domain | The set of all vectors x for which T(x) is defined.
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| * 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
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| * range | the set of all vectors of the form T(x) for some x in the domain of T.
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| *image, preimage | The vector T(x) assigned to x by T.
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| *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.
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Created by:
slonczt
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