Question

Let T:R^3>R^4 be the linear transformation given by the rule

T(x,y,z) = (3x+y-3z, y, x+y-z, -x+y+z)

Find the matrix A that represents T relative to the ordered bases
B={(1,1,1),(1,1,0),(1,0,0)}
and
B'={(1,0,0,0),(0,1,0,0),(0,0,1,1),(0,0,1,2)}
of R^3 and R^4 respectively