2. Consider an unknown linear transformation T that maps vectors from R to vectors in R....

 

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2. Consider an unknown linear transformation T that maps vectors from R to vectors in R. Although the transformation is unknown, we have been given its results when applied to the standard basis: Given: S = e = e2 = 1 e3 = T(e) = [2], T(e) = [], _T(3) = [0] a. Find a matrix A such that T(X) =Ax for all vectors x in R. b. Find T(X) for the case x = c. Find T(X) for the case x = Hint: Answer is the same for all linear transformations from R to R 2. Consider an unknown linear transformation T that maps vectors from R to vectors in R. Although the transformation is unknown, we have been given its results when applied to the standard basis: Given: S = e = e2 = 1 e3 = T(e) = [2], T(e) = [], _T(3) = [0] a. Find a matrix A such that T(X) =Ax for all vectors x in R. b. Find T(X) for the case x = c. Find T(X) for the case x = Hint: Answer is the same for all linear transformations from R to R