CS 3101N / Notes
Notes
Each unit written out from the lecture decks, to read before the drill asks about it: the definitions in order, the tables and formulas worth memorising, worked examples, and the mistakes that cost marks.
- U1Systems of Linear EquationsA system of linear equations has exactly one solution, infinitely many, or none, and row-reducing its augmented matrix tells you which. The exam asks you to spot a linear equation, write a solution set in parameters, carry out row operations in the R1 ↔ R2 notation, and solve by Gaussian elimination with back-substitution or by Gauss-Jordan elimination.
- U2Operations with MatricesMatrices get their own arithmetic: equality, sums and scalar multiples work entry by entry, but a product is rows times columns and only exists when the sizes fit. The exam asks you to compute these, write a system as Ax = b, and know which rules from ordinary algebra still hold and which break.
- U3The Inverse of a MatrixThe inverse of a square matrix A is the matrix A⁻¹ that undoes it: AA⁻¹ = A⁻¹A = I. The exam asks you to decide whether A⁻¹ exists, find it with the ad − bc formula or by row-reducing [A | I], use its properties, and solve Ax = b as x = A⁻¹b.
- U4DeterminantsEvery square matrix has a number attached to it, its determinant. The exam asks you to find a 2 × 2 determinant, the minors and cofactors of a 3 × 3 or 4 × 4, a determinant by cofactor expansion along the row or column with the most zeros, and a triangular determinant by multiplying the main diagonal.
- U5Vector SpacesA vector is an ordered list of numbers you can add and scale, and a vector space is any set where those two operations obey the same ten rules they obey in Rⁿ. The exam asks you to compute with vectors in Rⁿ, write one vector as a linear combination of others, show a set is not a vector space by naming the axiom that fails, and test whether a subset is a subspace.