Section outline

  • General

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  • Course Materials

    • Lecture Notes Folder

      The 14 lectures will cover the material as broken down below (with the relevant pages in the lecture notes):

      1-3: Linear Systems, Matrix Algebra (pages 3-20)

      3-4: Inverses and Transposes (pages 21-24)

      4-5: Vector Spaces and Subspaces (pages 25-33)

      6: Bases (pages 34-43)

      7-8: Dimension (pages 46-51)

      9-10: Linear Maps. Rank-Nullity Theorem (pages 52-60)

      11-12: Matrices representing Linear Maps (pages 61-68)

      13-14: Inner Product Spaces (pages 69-77)

    • Sheet 1 Assignment

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

      Systems of linear equations

      Matrix algebra 

    • Sheet 2 Assignment

      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

    • Sheet 3 Assignment

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

      Vector spaces and subspaces

      Linearly independent sets

      Spanning sets

      Bases

    • Sheet 4 Assignment

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

      Bases

      Dimension

      The dimension formula

      Direct Sums

    • Sheet 5 Assignment

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

      Linear Transformations

      Kernels

      Images

      Rank-Nullity Theorem


    • Sheet 6 Assignment

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

      Matrices representing Linear Transformations

      Change of Basis

      Row and Column Rank


    • Sheet 7 Assignment

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

      Bilinear Forms

      Inner Product Spaces