ABSTRACT
The strategy for solving an arbitrary system is to find an upper-triangular system equivalent with it and solve this upper-triangular system using back substitution. Essentially the same procedure may be used in case the coefficient matrix is not square. If the coefficient matrix is not square, we may make it square by appending either rows or columns of 0s as needed. The collection of all column vectors with real components is Euclidean n-space. A collection of eigenvectors corresponding to different eigenvalues is necessarily linear-independent. The most important property of the determinant is the fact that a matrix in invertible if and only if its determinant is not zero.
