*** A vector v = (x,y,z) with horizontal coordinates is a has been considered as a 1x3 matrix. Its transpose v^T is a vector with vertical coordinates and is a 3x1 matrix. Using vertical vectors the equations (*) 2x + 3y + z = 14
x + 2y + 4z = 12
3x - y + 3z = 6 may be written in a more convenient matrix notation which uses the coefficient matrix directly:
The sizes make the matrices conformable for multiplication:
                         ***