In some cases, however, you may prefer to convert the system of linear equations into a matrix equation, and then apply matrix manipulation operations to solve it. This approach is often useful when the system of equations arises as part of a general algorithm, and you do not know in advance how many variables will be involved.
The vector and tensor case is more complicated because of the need to account for the change of basis vectors.
American Mathematical Society
Source: MSC2010 database
Source: AC3D – Wikipedia