Linear Equations and Matrix Calculations

This lecture covers the fundamentals of linear equations and matrix calculations, introducing matrices as rectangular arrays of real numbers. It explains matrix notation, matrix operations such as addition and scalar multiplication, and matrix multiplication. The lecture also delves into systems of linear equations, defining them as sets of equations that can be represented in matrix form. It discusses the properties of matrix operations, the power of a matrix, and the solution of linear systems through matrix operations. The lecture concludes with the concept of equivalent matrices and the use of elementary row operations to solve systems of linear equations.