If one has linear equations such as a+b+c = 0, d = 5, a + c + d = 1, c + b = 6, one can represent them in a matrix, and then use Gaussian Elimination to quickly solve for the variables. But how does one represent these equations in a matrix: a + b = 0, a*b + c + d = 0, a*d + c*b = 0, c*d = 4?