Problem:
1. Constructing a linear transformation from vectors.
Is there a linear transformation T in R^3 → R^3 for which:
(2) (4)
T (1) = (1)
(3) (9)
(3) (9)
T (1) = (1)
(0) (1)
T (3) (9)?
(2) = (4)
(3) (9)
If there is, give the transformation formula, and the associated 3 by 3 matrix. If there isnt, explain in detail why there isnt.