M1: Linear Algebra I (202223)
Topic outline


The 14 lectures will cover the material as broken down below (with the relevant pages in the lecture notes):
13: Linear Systems, Matrix Algebra (pages 320)
34: Inverses and Transposes (pages 2124)
45: Vector Spaces and Subspaces (pages 2533)
6: Bases (pages 3443)
78: Dimension (pages 4651)
910: Linear Maps. RankNullity Theorem (pages 5260)
1112: Matrices representing Linear Maps (pages 6168)
1314: Inner Product Spaces (pages 6977)

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
RankNullity 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
