Homework Statement
Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively.
Find the standard matrix of T and determine whether T is one to one and if T is onto
Homework Equations
The Attempt...
Homework Statement
Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively.
Find the standard matrix of T and determine whether T is one to one and if T is onto
Homework Equations
The Attempt...
I know T(x) =Ax=[T(e1) ,T(e2,) T(e3)]
I thought A would just be the matrix with columns (1,1,1) (0,1,3) and (3,4,0), but then I realized that
(1,1,0) ,(1,0,1) and (0,1,1) are not the standard basis vectors for R3
My book doesn't give any examples where we don't start with the standard basis...
Homework Statement
Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively.
Find the standard matrix of T and determine whether T is one to one and if T is onto