MATH136 Lecture 4: Week 4 (lec 10-11) Lecture Notes
3 Feb 2012
School
Department
Course
Professor
34
MATH136 Full Course Notes
Verified Note
34 documents
Document Summary
A system of linear equations is homogeneous if the rhs contains only zeros. (ie. the augmented matrix is of the following form: . ) Has the trivial solution as the only solution. Note: we can write the solution set as. The solution set of a homogeneous with equations in variables, subspace of . The rank of a matrix is the number of leading ones in the rref of the matrix. Let be the augmented matrix of a system of linear equations with equations in variable. If the rank is less than the rank of , then the system is inconsistent. If the system is consistent, then has free variables. A consistent system has a unique solution iff. If , then the system is consistent for every . Let be the rref of , be the rref of . If then has a row of the form .
