Lecture 5 Solution Sets of Linear Systems (Completed)

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School
Pennsylvania State University **We aren't endorsed by this school
Course
MATH 220
Subject
Mathematics
Date
Oct 16, 2023
Pages
11
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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) ቎ 1 0 0 0 1 0 0 0 1 ቮ 3 −2 5 ቏ (2) ቎ 1 0 0 0 1 0 ቮ −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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