MAM2000W (MAM2000W)

Detailed and understandable summary of the Basis of a Vector Space/Subspace. Packed with exam problems and colourful hints. Contains: - Basic explanation of a Basis and Dimension of a Basis - Detailed method for basis of the column space, a span of vectors, null space, general subspace, and row space - 1 Example to find basis of span - 1 Examples to find basis of general subspace - Definition of Row space - Explanation of dimensions of vector spaces - Standard basis of vector spaces and polynom...

Detailed and understandable summary of Markov Chains and Steady State Vectors. Packed with examples and colourful hints. Contains: Detailed explanation Markov Chains - Transition diagrams - 1 Detailed Example - Initial and Future state vectors - Transition Matrices - Steady state vectors explained and formula - 1 Example of finding the steady state vector

Detailed and understandable summary of The Rank-Nulity Theorem. Packed with examples and colourful hints. Contains: Detailed explanation of the Rank-Nulity Theorem - How the results of the Rank-Nulity Theorem are added to the Invertible Matric Theorem - 9 Easy to Complex examples of applying the Rank-Nulity theorem.

Detailed and understandable summary of Invertible Matrices and The Invertible Matrix Theorem. Packed with examples and colourful hints. Contains: Notation - 2x2 Inverse - 2 Examples of 2x2 inverse - 3x3 Inverse by row equivalence and expansion formula - 4 Examples of 3x3 case for both methods - Properties of inverse matrices - The invertible matrix theorem detailed breakdown - 4 Application questions on the invertible matric theorem.

Detailed and understandable summary of Vector Spaces and Subspaces Packed with exam problems and colourful hints. Contains: - Detailed definition of a vector space - Closure of vector spaces - 10 Axioms - 7 Examples of proving sets of elements are vector spaces - Explanation of The Span to prove Subset Theorem - 4 Examples of prior theorem - Detailed explanation of the null space, column space with 2 examples each - Differences between null space and column space

Detailed and understandable summary of Eigenvalues, Eigenvectors and Diagonalization. Packed with examples and colourful hints. Contains: Important notation -Detailed method to find eigenvalues and eigenvectors - Eigenspaces - 2 detailed and annotated examples - All possible question types for eigenvalues and eigenvectors explained - Clear explanation of diagonalization - Detailed method of Diagonalization - 1 Example of Diagonalization

Detailed and understandable summary of Determinants and Cramer's Rule. Packed with examples and colourful hints. Contains: Explanation and notation of determinants - 2x2 determinant case - 3x3 determinant case by cofactor expansion via column or row - 2 Examples of cofactor expansion - Determinants of triangular matrices - Effects of row operation on determinants - Cramer's Rule explanation - 3 Examples of Cramer's Rule - Cramer's Rule for inverse matrices, with examples.

Detailed and understandable summary of Coordinates with respect to a basis. Packed with examples and colourful hints. Contains: Important notation - An explanation of the coordinate system - The Standard basis - Basis of polynomials - 3 Examples of all possible variations (find coordinate vector, basis or vector) - Change of coordinates between two different basis.

Detailed and understandable summary of how to Solve Matrices. Packed with exam problems and colourful hints. Contains: - Types of row operations - Row echelon form and Reduced Row echelon form - Row echelon terminology - Types of solutions - Parametric form for solution (detailed) - Elementary matrices - Inverse elementary matrices - Row equivalence