Section outline

    • The 14 lectures will cover the material as broken down below:

      1-3: Linear Systems, Matrix Algebra

      3-4: Inverses and Transposes

      4-5: Vector Spaces and Subspaces 

      6: Bases 

      7: Dimension 

      8: Dimension and Subspaces 

      9-10: Linear Maps. Rank-Nullity Theorem 

      11-12: Matrices representing Linear Maps 

      13-14: Inner Product Spaces 

    • This sheet corresponds to material covered in lectures 1 and 2, namely 

      Systems of linear equations

      Matrix algebra 

    • These problems correspond to material covered in lectures 3 and 4, in particular

      RRE form

      Transposes and Inverses

      Invertibility of EROs

      Process with EROs for determining invertibility

    • These problems correspond to material covered in lectures 5 and 6, in particular

      Vector spaces and subspaces

      Linearly independent sets

      Spanning sets

      Bases

    • These problems correspond to material covered in lectures 7 and 8, in particular

      Bases

      Dimension

      The dimension formula

      Direct Sums

    • These problems correspond to material covered in lectures 9 and 10, in particular

      Linear Transformations

      Kernels

      Images

      Rank-Nullity Theorem


    • These problems correspond to material covered in lectures 11 and 12, in particular

      Matrices representing Linear Transformations

      Change of Basis

      Row and Column Rank


    • These problems correspond to material covered in lectures 13 and 14, in particular

      Bilinear Forms

      Inner Product Spaces


    • A historical dissertation on the ancient Chinese methods for solving linear systems of equations.