Consider the map T : R3 → R3 given by T(x, y, z) = (x − 2y + z ,−3y + 2z, − x − y + z)    Choose only one answer as correct. (a) The matrix of this linear transformation in the base β = {(1, 0, 0),(0, 1, 0),(0, 0, 1)} is given by (image) (b) T is a one-to-one linear transformation which is equivalent to saying that Ker(T)={(0, 0, 0)}. (c) T is a surjective linear transformation, since the image of T, Im(T), has dimension 3. Thus, Im(T) = R3. (d) T is a linear transformation whose kernel, Ker(T), is a 1-dimensional vector subspace generated by vector (1, 2, 3). So T is one-to-one

Consider the map T : R³ → R³ given by T(x, y, z) = (x − 2y + z ,−3y + 2z, − x − y + z) 

Choose only one answer as correct.

(a) The matrix of this linear transformation in the base β = {(1, 0, 0),(0, 1, 0),(0, 0, 1)} is given by (image)

(b) T is a one-to-one linear transformation which is equivalent to saying that Ker(T)={(0, 0, 0)}.

(c) T is a surjective linear transformation, since the image of T, Im(T), has dimension 3. Thus, Im(T) = R³.

(d) T is a linear transformation whose kernel, Ker(T), is a 1-dimensional vector subspace generated by vector (1, 2, 3). So T is one-to-one