Solution sets of linear systems  Linear Equations with Matrices
Solution sets of linear systems
Lessons
Notes:
A system of linear equations is homogeneous if we can write the matrix equation in the form $Ax=0$.
A system of linear equations is nonhomogeneous if we can write the matrix equation in the form $Ax=b$.
We can express solution sets of linear systems in parametric vector form.
Here are the types of solutions a homogeneous system can have in parametric vector form:
1. With 1 free variable: $x=tv$
2. With 2 free variables: $x=su+tv$
3. With n free variables: $x=av_1+bv_2+\cdots+nv_n$
Here are the types of solutions a nonhomogeneous system can have in a parametric vector form:
1. With 1 free variable: $x=p+tv$
2. With 2 free variables: $x=p+su+tv$
3. With n free variables: $x=p+av_1+bv_2+\cdots+nv_n$

Intro Lesson
Solution Set of Linear Systems Overview: