M1: Linear Algebra I (2022-23)

Topic outline

• Select topic General

  General

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  • Select activity Announcements

    

    Announcements Forum
  • Select activity Prelims Mathematics Syllabus

    

    Prelims Mathematics Syllabus File
  • Select activity Mathematics and Philosophy Syllabus

    

    Mathematics and Philosophy Syllabus File
• Select topic Course Materials

  Course Materials
  • Select activity Lecture Notes

    

    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)
    

  • Select activity Sheet 1

    

    Sheet 1 Assignment

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

    Systems of linear equations

    Matrix algebra 

  • Select activity Sheet 2

    

    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

  • Select activity Sheet 3

    

    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

  • Select activity Sheet 4

    

    Sheet 4 Assignment

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

    Bases

    Dimension
    

    The dimension formula

    Direct Sums

  • Select activity Sheet 5

    

    Sheet 5 Assignment

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

    Linear Transformations

    Kernels

    Images

    Rank-Nullity Theorem

    
    

  • Select activity Sheet 6

    

    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

    
    

  • Select activity Sheet 7

    

    Sheet 7 Assignment

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

    Bilinear Forms

    Inner Product Spaces