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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 [26]. An initial introduction to matrices
and linear algebra can be found in [49].
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