2/4 90% II) Consider the standard basis e1, e2, e3, es of R. Suppose the linear T: R → R satisfies T(e1) = T(e2) = 2. T(es) = T(e4) = 1 4. What is the dimension of its range? III) If T: Mat3.2(F) →...

Only need part III

Extracted text: 2/4 90% II) Consider the standard basis e1, e2, e3, es of R. Suppose the linear T: R → R satisfies T(e1) = T(e2) = 2. T(es) = T(e4) = 1 4. What is the dimension of its range? III) If T: Mat3.2(F) → Mat2,2 (F) is a linear map whose null space has dimension 2, what is the dimension of its range? IV) If A E M33(R), call TA : R' → R' the linear operator whose matrix in the