Consider the linear system of equations
in matrix form:
This can be written in higher level form as
where

denotes the two-by-two matrix above, and

and

denote the two-by-one vectors. The solution to this equation
is then
The general two-by-two matrix inverse is given by
and the inverse exists whenever

(which is called the
determinant of the matrix

) is nonzero. For larger
matrices,
numerical algorithms are used to invert matrices, such as used by
Matlab
based on LINPACK [
25]. An initial introduction to matrices
and
linear algebra can be found in [
47].
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