Math 3108: Linear Algebra
                          Instructor: Jason Murphy
                      Department of Mathematics and Statistics
                     Missouri University of Science and Technology
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      Contents.
         ◮ Chapter 1. Slides 3–70
         ◮ Chapter 2. Slides 71–118
         ◮ Chapter 3. Slides 119–136
         ◮ Chapter 4. Slides 137–190
         ◮ Chapter 5. Slides 191–234
         ◮ Chapter 6. Slides 235–287
         ◮ Chapter 7. Slides 288–323
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                  Chapter 1. Linear Equations in Linear Algebra
       1.1 Systems of Linear Equations
       1.2 Row Reduction and Echelon Forms.
       Our first application of linear algebra is the use of matrices to
       efficiently solve linear systems of equations.
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            Alinear system of m equations with n unknowns can be
            represented by a matrix with m rows and n + 1 columns:
            The system
                                                a x +···+a x =b
                                                  11 1                     1n n            1
                                                     .                     .             .
                                                     .                     .             .
                                                     .                     .             .
                                                a      x +···+a x =b
                                                  m1 1                      mn n             m
            corresponds to the matrix
                                                        a             · · ·     a        b       
                                                               11                  1n         1
                                                        .                         .         .    
                                         [A|b] =              .                   .          .    .
                                                               .                   .         .
                                                            a          · · ·    a           b
                                                              m1                  mn           n
            Similarly, every such matrix corresponds to a linear system.
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