Created Revision Material
Breakdown topic patterns, create exemplar solutions based on the practical solutions, include all topics (even those without questions on mid-terms previously) - just in case.
- Linear Algebra Topics Patterns,
- Linear Algebra Exemplar Solutions,
- Linear Algebra Cheat Sheet,
- Linear Algebra Cheat Sheet (AI-GENERATED).
Given Revision Material
2023 Mid-Term Example Paper.pdf.
Week by Week Content
Week 19
Linear Algebra - Presentation 1.pdf Linear Algebra - Practical 1.pdf Linear Algebra - Practical 1 (solutions).pdf
- Vector Operations: Vector addition and scalar multiplication
- Linear combination of vectors
- Properties
- The span of two vectors in the plane
- Covering the plane
- Linear independence
Week 20
Linear Algebra - Presentation 2.pdf Linear Algebra - Practical 2.pdf Linear Algebra - Practical 2 (solutions).pdf
- Vector Operations: Vector addition and scalar multiplication in higher dimensions
- Span of vectors in higher dimensions
- Linear Independence
- Dot product and properties
- Length and angle of vectors
- Angle formula and inequalities
Week 21
Linear Algebra - Presentation 3.pdf Linear Algebra - Practical 3.pdf Linear Algebra - Practical 3 (solutions).pdf
- Introduction to Linear Systems
- Solution Sets
- Elimination Process
- Gauss-Jordan Elimination
- Elimination in Matrix Notation
- Row Echelon Form (REF)
- Reduced Row Echelon Form (RREF)
- Homogeneous Systems
- Theorem on Homogeneous Systems
- Examples of homogeneous systems and their solution sets
Week 22
Linear Algebra - Presentation 4.pdf Linear Algebra - Practical 4.pdf Linear Algebra - Practical 4 (solutions).pdf
- Introduction to Matrices
- Operations of Matrices: Addition and Multiplication
- Identity and Diagonal matrices
- Matrix Powers
- Transpose of a Matrix
- Symmetric and Triangular Matrices
- Rank
Week 23
Linear Algebra - Presentation 5a.pdf Linear Algebra - Presentation 5b.pdf Linear Algebra - Practical 5.pdf Linear Algebra - Practical 5 (solutions).pdf
- Introduction to invertible matrices
- Theorem and Proposition
- Inverse and determinant of a 2x2 matrix
- Properties of the Inverse
- Inverse of a matrix with Gauss-Jordan elimination
- Determinant of a 3x3 matrix
- Cofactor expansion
- Definition of determinants
- Properties of Determinants
- Volume and Determinants
- Cramer’s Rule (Solving linear systems with determinants)
Week 24
Linear Algebra - Presentation 6.pdf Linear Algebra - Practical 6.pdf Linear Algebra - Practical 6 (solutions).pdf
- Vector Spaces
- Vector Subspaces
- Proposition
- Basis
- Dimension
- Theorem
- Application to Matrices
- Row space, Column space and Null space
- Rank Theorem
- The fundamental Theorem of Invertible Matrices
Week 25
Linear Algebra - Presentation 7a.pdf Linear Algebra - Presentation 7b.pdf Linear Algebra - Practical 7.pdf Linear Algebra - Practical 7 (solutions).pdf
- Eigenvalues, Eigenvectors and Eigenspaces of a Matrix
- An experiment
- Remarks and properties
- Diagonalisation of matrices
- Theorem
- Geometric & Algebraic multiplicity
- Conditions for diagonalisation
- nth power of a matrix