Why say A times X is a combination of the columns of A?

How to understand

When I watching this tutorial of linear algebra, at 38:40 moment,

Gilbert Strang say:

A times X is a combination of the columns of A.

I don't understand this sentence, in my option, A is combination of each column of A, why there say A times X is a combination of the columns of A?

Just calculate

$\left( \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{matrix} \right)\left( \begin{matrix} x \\ y \\ z \\ \end{matrix} \right)=\left( \begin{matrix} x+2y+3z \\ 4x+5y+6z \\ 7x+8y+9z \\ \end{matrix} \right)=x\left( \begin{matrix} 1 \\ 4 \\ 7 \\ \end{matrix} \right)+y\left( \begin{matrix} 2 \\ 5 \\ 8 \\ \end{matrix} \right)+z\left( \begin{matrix} 3 \\ 6 \\ 9 \\ \end{matrix} \right)$

It gives an interesting viewpoint; the solution of $Ax=b$ is now "can b be a linear combination of the columns of A?" or "Is b in the span of the columns of A?". If b is not in this subspace, what is the closest point in the subspace to b, is then a natural question (the least squares solution of $Ax=b$).