SOLUTION: Let T:R^3➜R^2 be defined as T(x, y, z) = (x+y, y-z). Is T Invertible? How can you justify your answer?

Question 1182431: Let T:R^3➜R^2 be defined as T(x, y, z) = (x+y, y-z).
Is T Invertible?
How can you justify your answer?
Answer by ikleyn(52784) (Show Source): You can put this solution on YOUR website!
.


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    DOES  NOT  EXIST.

Solved and explained.

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