MATH125 Lecture 9: 09

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

Give an example of two lines which are (a) parallel (b) coincide. The discussion above suggest that a system of linear equations has either: no solutions, exactly one solution, in nitely many solutions. A system of linear equations is said to be consistent if it has at least one solution, i. e. either one solution or in nitely many; a system is inconsistent if it has no solutions. Two linear systems are called equivalent if they have the same solution sets. That is, each solution of the rst system is a solu- tion of the second one and conversely. { x y = 1 x + y = 3 and { x y = 1 y = 1 are equivalent since they both have the unique solution [2, 1]. Our approach to solving a system of linear equations is to transform the given system into an equivalent one that is easier to solve.