20Linear Systems
Linear systems are often solved by matrix methods. Grassmann showed how to do it using the outer product. The method is not especially efficient, being much the same as Cramer's method1.
20.1 Theory
In his book, Grassmann (1995) takes a system of linear equations as in Eq. (20.1), with unknown values 
and known scalar2 coefficients 
, and multiplies each row by a different primal unit:
That produces the system (20.2) in which each column has a common factor 
but different coefficients and primal units:
Leaving aside the common factors, Grassmann defined vectors 
from each column as in Eq. (20.3):
Then he rewrote the original linear system (20.1) as a linear combination of the vectors3:
Grassmann developed the solution for the first of ...
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