Systems of L E

Systems of L E

1. LINEAR EQUATION

2. SYSTEMS OF LINEAR EQUATIONS

3. SOLUTION SET

   • A SET CONTAINS ALL THE SOLUTIONS
   • ''NOTATION''
   • POSSIBILITIES OF SOLUTIONS
   • POSSIBILITIES IN VISUALISATION
   • EQUALITY OF SYSTEMS
     • SEEN FROM SOLUTION SET
   • CONSISTENT SYSTEM
     • WHAT IS IT ABOUT
     • E.G. HOMOGENOUS SYSTEM

4. PROCESSING AS MATRIX APPLICATION

   • AUGMENTED MATRIX
   • RELEVANTS
     • Carl Fredrich Gauss
     • COEFFICIENT MATRIX
     • ROW EQUIVALENCE. OR EQUALITY UPON 2 SYSTEMS.
     • GUESS ABOUT WHY REF WORKS
       • BACK SUBSTITUTION
   • REF
     • CONDITIONS.
     • NON-UNIQUE
   • G.E.
     • USE EROs : M -> REF, THEN (BACK SUB) OR (WHATEVER)
     • KEY OF CALCULUS
       • REWRITE THE FORM INTO AM
       • OBTAIN REF
         • RULES: EROs
         • INTRODUCE ''0''
       • THE LAST STEP
         • ONE SOLUTION: BACK SUB
         • OR INFINITE: FREE VARIABLES AS DIMENTIONS
   • RANK
     • SEE IN REF: #(NON ZERO ROWS) OR #(LEADING ENTRIES)
     • #(FREE VARIABLES) = #(VARIABLES) - RANK
   • R.REF
     • CONDITIONS.
       • FROM REF
       • LEADING ENTRY SHOULD BE 1
       • LEADING 1 AND 0 ELSEWHERE IN THAT COLUMN
         • IF NO LEADING 1 THEN THAT'S ALL FINE
     • UNIQUE, ORDERED STUFF