Let T:R 3→R 3
be the linear operator defined by T(x 1 ,x 2 ,x 3
)=(x 1 −x 2 ,x 2 −x 1,x 1−x 3
) a. Find the matrix for the linear transformation T with respect to the basis B={v 1 ,v 2 ,v 3}, wherev 1 =(1,0,1),v 2=(0,1,1),v 3=(1,1,0)
b. Verify that Formula (8) holds for every vector in R 3. c. Is T one-to-one? If so, find the matrix of T −1
with respect to the basis B.
