4.1.8

Let $$v$$ be a $$m$$-dimensional column vector, because $$A$$ has rank 1 it is of the form $$\begin{bmatrix} v & \alpha_0 v & \alpha_1 v & \dots & \alpha_n v \end{bmatrix}.$$ Now let $$X = v$$ and $$Y = (1, \alpha_0, \dots, \alpha_n)^t,$$ then we get $$A = XY^t.$$