Introductionto
                               LinearAlgebra
                                RubénPérezSanz
                           UniversitatAutònomadeBarcelona
                                September22,2020
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                            TableofContents
       1. MatrixandVectorAlgebra
          SystemsofLinearEquations
          Vectors
          MatricesandMatrixOperations
          MarixMultiplication
          TheTranspose
       2. Determinantsandinversematrices
          Determinants
          3orderDeterminants
          Determinantsrules
          InverseofaMatrix
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                             SYSTEMSOFLINEAREQUATIONS
           Previously we have seen how to solve a very simple system of
           equations,namelyalinearsystemwith2equationsand2unknowns.
           The way these systems are solved are quite straight forward.
           However, when we have systems of 3,4,... or n equations we need
           amoresystematicwaytosolvethem.
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                   SYSTEMSOFLINEAREQUATIONS
       In this sense is crucial to understand the notation at hand. We will
       considerasystemofmequationsandnunknownsx1,x2,...,xn :
                         a11x1 + a12x2 + ... + a1nxn = b1
                         a21x1 + a22x2 + ... + a2nxn = b2                   (1)
                                      ...............
                        am1x1 + am2x2 + ... + amnxn = bm
       Where a11,a12,...,amn are the coefficients of the system, and
       b1,...,bm are called the right-hand sides.
       Note:
         1. Theequationsarelinearintheunknowns
         2. Oneormorecoefficientsmightbe0
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