Nowadays we represent the system of $m$ linear equations
$$\sum\_{i=1}^na\_{1i}x\_i=y\_1$$
$$\sum\_{i=1}^na\_{2i}x\_i=y\_2$$
$$\vdots$$
$$\sum\_{i=1}^na\_{mi}x\_i=y\_m$$
as $\mathbf{Ax}=\mathbf{y}$, where $(A)\_{ij}=a\_{ij}$ is an $m\times n$ matrix, $\mathbf{x}$ is an $n\times 1$ column vector, and $\mathbf{y}$ is an $m\times 1$ column vector. Call this the "column picture." But we could just as well have represented it by the transposed equation
$$\mathbf{y}^T=\mathbf{x}^T\mathbf{A}^T$$
where we now deal with row vectors rather than column vectors. Call this the "row picture." I have two questions:

(1) Can anyone point to a specific historical reference in which a linear system of equations was represented using the row picture?

(2) Are there any deep reasons for preferring the column picture to the row picture? Or is it fair for us to describe the column picture as totally arbitrary?