Linear Algebra

What it covers

• Linear systems, Gaussian elimination, echelon forms
• Vector spans, linear independence, linear transformations
• Matrix algebra, invertibility (Invertible Matrix Theorem)
• Subspaces, column/null space, dimension, rank theorem, determinants
• Eigenvalues/eigenvectors, diagonalization, discrete dynamical systems
• Inner products, orthogonality, Gram-Schmidt, least-squares, spectral theorem

Assessment

Non-mandatory, non-resittable midterm plus a comprehensive 3h closed-book final exam, no calculators. If the midterm score beats the endterm and the endterm is ≥5.0: Final = 0.20×Midterm + 0.80×Endterm; otherwise Final = Endterm. The exam has a multiple-choice/short-answer part and an "Academic Reasoning" (proofs) part.

Resources

• Essence of Linear Algebra – 3Blue1Brown — geometric intuition.

Worth knowing

• Strict closed-book, no-calculator policy.
• Recurring proof strategy recommended in the material: "Recall, Try, Answer" for Academic Reasoning questions.
• Past papers recur on the same themes: Rank-Nullity, basis checks, chains through the Invertible Matrix Theorem.
• The midterm can only help your grade (weighted 20% when it beats the endterm) — it never hurts it.