Visualizing Linear Systems Ex:Sketch the linear system 𝑥 − 2𝑦 = 1 3𝑥 + 2𝑦 = 11 . These lines: Therefore the linear system has: Use Gauss Jordan elimination on the corresponding augmented matrix to determine the coordinates of the point of intersection. Lecture 5: Solution Sets of Linear Systems Math 220 Fall 2023 Lecture Notes Page 1

How to find the unique solution of a linear system: Complete Gauss Jordan elimination. •Verify there is a pivot in every column of the coefficient matrix. In reduced echelon form we are looking for exactly one leading 1 in each column of the coefficient matrix and only zeros for all other entries in those columns. •Convert each row back to an equation that determines the value of one of the variables. •Ex:Determine the solution of each linear system. (1) 100010001ቮ3 −2 5 (2) 100010ቮ−6 8 0 Math 220 Fall 2023 Lecture Notes Page 2

Ex:Sketch the linear system 𝑥 − 2𝑦 = 1 −𝑥 + 2𝑦 = 3 . These lines: Therefore the linear system has: Use Gauss Jordan elimination on the corresponding augmented matrix to determine what to look for in an augmented matrix that would indicate a linear system has no solution. Math 220 Fall 2023 Lecture Notes Page 3

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