Heres the question:
Let be defined by T(a,b,c) = (a+b, b-2c, a+2c). Determine if the vector v=(2,1,1) exists in R(T) [the range].
Heres what I got:
The matrix corresponding to this system is:
A=
After some row operations...
A=
Then I computed the augmented matrix (A|b) and simplified to:
(A|b)=
So the rank(A)=2 and rank(A|b)=2.
By a theorem, this system is consistent ( the solution set is nonempty)
Does this mean that the vector v exists in R(T), and why?