2. Linear algebra
     1. Systems of linear equations (SLEs). Matrix operations
     2. Solutions of SLEs by the Gauss elimination 
     3. Two‐dimensional arrays and operations with matrices in MATLAB
     4. Determinant and matrix inverse
     5. Solution of SLEs in MATLAB
     6. Summary
     Text
     A. Gilat, MATLAB: An Introduction with Applications, 4th ed., Wiley
     Wikipedia: Matrix, SLE, etc.
     ME 349, Engineering Analysis, Alexey Volkov                              1
     2.1. Systems of linear equations (SLEs). Matrix operations
      Systemsoflinearequations(SLEs)
      Notionofamatrix
      Operationswithmatrices
      Specialmatrices
      MatrixformofaSLE
     Readingassignment
     Gilat, 3.1, 3.2, 3.4, and 3.5
     ME 349, Engineering Analysis, Alexey Volkov                             2
         2.1. Systems of linear equations (SLEs). Matrix operations
                                                     Systems of linear equations
         The system of linear equations (SLE) of ݉	equations with ݊	unknowns is the system :
               ܽ ݔ ൅ܽ ݔ ൅⋯൅ܽ                         ݔ      ൅ܽ ݔ ൅ܽ               ݔ      ൅⋯൅ܽ ݔ ൅ܽ ݔ ൌܾ
                ଵଵ ଵ        ଵଶ ଶ               ଵ௝ିଵ ௝ିଵ          ଵ௝ ௝       ଵ௝ାଵ ௝ାଵ                ଵ௡ିଵ ௡ିଵ           ଵ௡ ௡         ଵ
              ܽ ݔ ൅ܽ ݔ ൅⋯൅ܽ                          ݔ      ൅ܽ ݔ ൅ܽ               ݔ      ൅⋯൅ܽ ݔ ൅ܽ ݔ ൌܾ
                ଶଵ ଵ        ଶଶ ଶ               ଶ௝ିଵ ௝ିଵ          ଶ௝ ௝       ଶ௝ାଵ ௝ାଵ                 ଶ௡ିଵ ௡ିଵ          ଶ௡ ௡         ଶ
                                                                         …                                                      (2.1.1)
              ܽ ݔ 	൅	ܽ ݔ 	൅⋯൅	ܽ                       ݔ     	൅	ܽ ݔ 	൅ܽ              ݔ      ൅⋯൅ܽ ݔ ൅ܽ ݔ ൌܾ
                ௜ଵ ଵ         ௜ଶ ଶ               ௜௝ିଵ ௝ିଵ           ௜௝  ௝ …     ௜௝ାଵ ௝ାଵ                ௜௡ିଵ ௡ିଵ          ௜௡ ௡        ௜
           ܽ    ݔ ൅ܽ ݔ ൅⋯൅ܽ                         ݔ      ൅ܽ ݔ ൅ܽ                 ݔ      ൅⋯൅ܽ               ݔ      ൅ܽ ݔ ൌܾ
             ௠ଵ ଵ         ௠ଶ ଶ               ௠௝ିଵ ௝ିଵ           ௠௝ ௝        ௠௝ାଵ ௝ାଵ                 ௠௡ିଵ ௡ିଵ            ௠௡ ௡          ௠
         ܽ , coefficients of equations (݅ൌ1,..,݉, ݆ൌ1,..,݊). ݉ is the number of equations.
          ௜௝
         ݔ , unknowns(݆ൌ1,..,݊). ݊ is the number of unknowns.
          ௝
         ܾ , right‐hand sides (RHSs) of equations (݆ൌ1,..,݉).
          ௝
         TosolveaSLEmeanstofindsuchݔ thatturneveryequationinthesystemintoidentity.
                                                        ௝
          Ingeneral, a SLE may have/not have a solution.
          Ifasolutionexits, it can be unique, or, alternatively, the system may have multiple solutions.
          Solution of SLEs is a fundamental mathematical problem. Multiple problems in science and
             engineering reduce to the solution of SLEs.
         ME 349, Engineering Analysis, Alexey Volkov                                                                                       3
     2.1. Systems of linear equations (SLEs). Matrix operations
     Example:SLEwithrespecttoforcesinatruss
                                                                       ܨ
                                                                        ଵଵ
     ME 349, Engineering Analysis, Alexey Volkov                             4