Another approach may be based on re-arrangement of equations 35 and 36. We assume the problem is to minimise . In the exact case

Hence, in the exact case, we compute the parameter vector x to be . In the case of Least Squares the product gives the best fitting approximation. However this assumes that the inverse of the matrix can be computed, which is not always the case. In general, the inverse of a square matrix exists, if, and only if, the matrix is non-singular, i.e. the determinant is not equal to zero. For example, we can consider again the case of the exact fit of a plane expressed by equation 37

and the inverse is the reciprocal of the determinant multiplied by the matrix of cofactors. Multiply this by to obtain the final answer, which is a very long expression, so consider a simple example.