MATH125 Lecture Notes - Lecture 12: Gaussian Elimination

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

Document Summary

It is important to note that row operations are reversible. If two rows are interchanged they can be returned to their original position by another interchange. If a row is multiplied by a nonzero constant, say c, then multiplying the new row by 1/c produces the original row. Also one can show that if we change a row by adding it with a multiple of another row we can return to the original state by using the same type of operation. This produces an important consequence: after application of a row operation each solution of a new system is also a solution of the original system and conversely. If the augmented matrices of two linear systems are row equiv- alent then the two systems have the same solution sets. When row reduction is applied to the augmented matrix of a sys- tem of linear equations we create an equivalent system that can be solved by back substitution.