UTSA Problem-Solving Club

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Linear Algebra

Spring 2026 · 10 problems

No one shall expel us from the paradise that Cantor has created.

David Hilbert

Matrix and linear-algebra problems in the competition style.

Download the problem set (PDF)

What is in it

Problems only — the club works these out together at meetings. Topic and attribution are listed as a starting point.

  1. The grazing cows System of linear equations
  2. The Commuting Converse Matrix InversesHard
  3. Skew-symmetry? That’s odd! Eigenvalues/vectorsMedium
  4. Cubic-to-Quadratic Putnam 1991 A2
  5. Putnam 1990 B3
  6. Additive translates in \(\mathrm{GL}_2(\mathbb{Z})\) Putnam 1994 A4
  7. Circle-in-Tesseract Optimization/Orthogonal MatricesPutnam 2008 B3
  8. Diverging GCDs Putnam 1994 B4
  9. Putnam 2018 A2
  10. \(\mathrm{GOE}_2\)