## Solving Linear Equations Using Matrices

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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