This is similar to the other problem. Given x = (x_{1}, ..., x_{n})^{T}, where the superscript T means transpose, i.e., this is a column vector, Ax = x_{1}A_{1}+ ... + x_{n}A_{n}where A_{i}is theith column of A and this is the sum of column vectors. The fact that x ↦ Ax is onto means that for every b ∈ ℝ^{n}there exist an x such that Ax = b. But this also means that the columns of A span ℝ^{n}.