Applied Mathematics 1411A/B Lecture Notes - Lecture 2: Augmented Matrix, List Of Forgotten Realms Nations, Gaussian Elimination

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Natalia Kiriushcheva

Document Summary

Recall: last day, we introduced gaussian and gauss-jordan elimination for row- reducing a matrix. More examples: let"s do some more examples of the end of the algorithmsuppose we row-reduced the augmented matrix corresponding to a linear system and obtained: Terminology: a leading variable is a variable that has a leading 1 in its column and a free variable is a variable that has no leading 1 in its column. Definition: a system of linear equations is said to be homogeneous if the constant terms are all zero. 0 ib for all i between 1 and n. xa. Every homogeneous system is consistent, because it has at least the solution x. Either there is only the trivial solution, or there are infinitely many solutions. A homogeneous system of equations with more unknowns than equations has infinitely many solutions. Example: determine the values of k for which the system of equations has: no solutions, exactly one solution, infinitely many solutions.