Math1002 Linear Algebra Revision

Description

Note: These are handwritten notes. This is a revision summarised from 21 lectures Topics Covered: ** VECTORS: - Draw vectors - Unit vectors - Parallel vectors - Cartesian form - Length of a vector - Linear independence of two vectors ** DOT PRODUCTS: - Algebraic definition - Geometric definition - Cauchy Schwarz Inequality - Dot product rules ** CROSS PRODUCTS: - Algebraic definition - Geometric definition - Cross product rules ** LINES L: - Parametric vector equation of L - Parametric scalar equations of L - Cartesian equation - From point to lines ** PLANES P: - Vector equation of a plane P - Cartesian equation of a plane P - From point to plane ** INTERSECTIONS: - Point of intersection of a line and a plane - Intersections of planes ** SYSTEMS OF LINEAR EQUATIONS: - Row Echelon Form examples - Reduced Row Echelon Form examples ** MATRICES: - Addition, subtraction, scalar multiplication - Powers of matrix - Matrices and systems of operations - Matrix inverses - Manipulating matrix equations - Determinants - Eigenvalues and Eigenvectors - Eigenspace - Diagonalisation