Applications of Matrices: Solving System of Linear Equations

Solving a system of linear equations is one of the most important applications of matrices and determinants. Such systems arise as mathematical models across biology, chemistry, commerce, economics, physics and engineering -- circuit-theory analysis, input-output economic models, and chemical-reaction balancing all reduce to solving one. This section develops three methods for a system whose coefficient matrix is square and non-singular -- matrix inversion (§1.4.3.1), Cramer's rule (§1.4.3.2), and Gaussian elimination (§1.4.3.3, which does not actually need that restri …