MATH136 Lecture Notes - Lecture 8: Row Echelon Form, Harmonic Oscillator, Coefficient Matrix

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Sproule

Document Summary

Wednesday, january 22 lecture 8 : systems of linear equations. Concepts: m linear equations in n unknowns (system of linear equations), solving a system of linear equations, equivalent system of linear equations, coefficient matrix, augmented coefficient matrix, rref coefficient matrix, pivot, leading-1, ref matrix. 8. 1 introduction linear equations are equations of the form a1x1 + a2x2 + + anxn = b. where the xi"s are called the variables, or unknowns, while the ai"s are the coefficients of the linear equation. The term b which is not juxtaposed to a variable is referred to as the constant. A system of linear equations is a finite set of linear equations each containing the same variables. Solving a system of linear equations means finding the set of all vector values x = (x1, x2, x3, , xn) that satisfy all of the given linear equations. In this lecture we discuss a method for solving these by manipulating only the coefficients and the constants.