Suppose that T: R^n ---> R^m is a linear transformation (n=2 or 3 and m=2 or 3). Suppose that x1, ..., xn is a basis for the domain of T. Show that T is surjective iff T(x1), ..., T (xn) is a spanning set in R^m.
So T(x1 + ... + xn) = T(x1) + ... + T(xn)
and T(cx1) = cT(x1)
But I'm not sure where this gets me and how it can relate to surjectivity.
So T(x1 + ... + xn) = T(x1) + ... + T(xn)
and T(cx1) = cT(x1)
But I'm not sure where this gets me and how it can relate to surjectivity.