Preimage.md (772B)
1 # Preimage 2 3 Khan Unit 2 4 5 **Definition:** The preimage of an image is the set of all values in the codomain such that their mappings are all in a specified image. This image may be the codomain or some other set. 6 7 T^-1(S) = Preimage of S under T. 8 9 This can also be stated as T'(S) 10 11 ## Finding 12 13 To find the preimage of some image under T we need to find all input vectors a such that T(a) is in the image. 14 15 If we specify the image as <1,2> and <0,0> then we need to find all <x_1,x_2> such that <x_1, x_2> x L.T. Matrix = <1,2> or <0,0>. 16 17 This final result can be found using [ReducedRowEchelonForm](ReducedRowEchelonForm.md) of both augmented matricies created using the above information where the result is the computed values of all pivot variables put into matricies.