ObsidianVault/College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.1 - Lines and Linear Equations.md

#uw/notes #uw/class/math208

---

• Possible intersections of 3 planes in 3D space
  • 1 point - one solution
    • z=0
    • x=0
    • y=0
  • 1 line - infinite solutions
    • z=0
    • x=0
    • x=z
  • 3 lines - no solutions
    • z=0 z=x+1
    • z=1-x
  • one plane - infinite solutions
    • z=0
    • 2z=0
    • 3z=0
  • no intersections - no solutions
    • z=0
    • z=1
    • z=2
• Adding constant multiple of one linear equation in system does not change solution set of system
  • concept behind gaussian elimination