Lecture 01:
 Linear system and Gauss elemination,3x3 case.
 augmented matrix
 matrix indexing convention
 column
 row

 Gauss elemination and elementary row operations
 Row echlon form and gauss eleimnation
 determine solvability from row echelon form
  case 1
   if kth row = idnetiacally zero and b_k not=0, then no solution
  case 2
   if not case 1, then solvable
 choice of essestial and free variables and Row echelon form
 counter example of choosing essential variables the wrong way
Lecture 02:
 elaborate on the inconsisntency resulting from wrong chice of free variables
 examples: traffic.
 
 matrix algebra: matrix multiplication