Question 1182431
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Notice that T is a linear map of R^3 to R^2.


No one such linear map from R^3 to R^2 can be invertible.


Just because many different elements of R^3 map into the same element of R^2.


For example, many different elements of R^3 map to 0 (zero) element of R^2.


    More concretely, all the vectors  of the form  (x,y,z) = (x,-x,-x)  for any real value of  x  map into  0 (zero) by the map T.


It means that the inverse map  {{{T^(-1)}}}  DOES  NOT  EXIST.
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Solved and explained.