M1: Linear Algebra I (2022-23)
Section outline
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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)
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This sheet corresponds to material covered in lectures 1 and 2, namely
Systems of linear equations
Matrix algebra
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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
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These problems correspond to material covered in lectures 5 and 6, in particular
Vector spaces and subspaces
Linearly independent sets
Spanning sets
Bases
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These problems correspond to material covered in lectures 7 and 8, in particular
Bases
Dimension
The dimension formula
Direct Sums
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These problems correspond to material covered in lectures 9 and 10, in particular
Linear Transformations
Kernels
Images
Rank-Nullity Theorem
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These problems correspond to material covered in lectures 11 and 12, in particular
Matrices representing Linear Transformations
Change of Basis
Row and Column Rank
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These problems correspond to material covered in lectures 13 and 14, in particular
Bilinear Forms
Inner Product Spaces
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