Applied Mathematics 1411A/B Lecture Notes - Lecture 1: Global Positioning System, Solution Set, Gaussian Elimination

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Introduction to systems of linear equations (1. 1; pg. 2) Definition: a linear equation in the n variables, equation that can be written in the form: xa. 2 n ia are called the coefficients, and the and b are real constants. If it cannot be written in this form, it is where. Application: suppose that is invested in 3 stocks. If a , b, and c, denote the number of shares of each stock that are purchased and they have units costs , . 5, and. respectively, write the linear equation describing this scenario. Definition: a solution of a linear equation (or n-tuple) of n numbers substitute equation is called the solution set (or sometimes the general solution) of the equation. Example: ns such that the equation is satisfied when we in the equation. The set of all solutions of the n s , s s x is a sequence xa.

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