Abstract
This chapter discusses determinants and linear equations. The theory of linear systems is the basis and a fundamental part of linear algebra, a subject that is used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well. The determinant provides important information about a matrix of coefficients of a system of linear equations or about a matrix that corresponds to a linear transformation of a vector space.
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