Using Challenging Problems in Teaching Linear Algebra

  • Abraham BermanEmail author
Part of the ICME-13 Monographs book series (ICME13Mo)


We present examples of interesting problems that hopefully make the learning and the teaching of linear algebra enjoyable. The problems are on matrix multiplication, rank, determinants, eigenvalues and eigenvectors, and matrices and graphs. The problem solving strategies used include “look for invariants”, “check parity” and “define an energy function”.


Teaching through problem solving Teaching problem solving Teaching linear algebra 


  1. Berman, A., & Kon, B.(2002). Linear Algebra (in Hebrew) BAK, Haifa.Google Scholar
  2. Carlson, D., Johnson, C., D. Lay, D., & Porter, A.D. (2002). Linear Algebra Gems. The Math Association of America., Notes Series No. 59.Google Scholar
  3. Fi, C. & Degner, K. (2012). Teaching through problem solving, Mathematics Teacher, Vol. 105, No. 6, 455-459.Google Scholar
  4. Halmos, P. R. (1995). Linear Algebra Problem Book, Dolciani Mathematical Expositions No 16, The Mathematical Association of America.Google Scholar
  5. Klinstern, M. (2016). Problem Posing and Choosing Problems by High School and University Mathematics Teachers. Ph.D dissertation, Technion.Google Scholar
  6. Lester, F. (1994). Musing about mathematical problem solving research: 1970-1994, Journal for Research in Mathematics Education 25, 660-675.Google Scholar
  7. Matousek, J. (2010). Thirty Three Miniatures Mathematical and Algorithmic Applications of Linear Algebra, Student Mathematical Library, Vol 53, American Mathematical Society.Google Scholar
  8. Moran, G. (1995).On the Period-Two-Property of the majority operators in infinite graphs, Transaction of the American Mathematical Society. Vol. 347, No. 5, 1649-1667.Google Scholar
  9. Polya, G.(2004). How to solve it, 1945; with foreword and added exercises by Y. Conway, Princeton University Press.Google Scholar
  10. Prasolov, V. (1994). Problems and Theorems in Linear Algebra, Translations of Mathematical Monographs, Vol 134, American Mathematical So ciety.Google Scholar
  11. Schoenfeld, A. (1985). Mathematical Problem Solving, Academic Press.Google Scholar
  12. Zhang, F. (1996). Linear Algebra Challenging Problems for Students, Johns Hopkins.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsNational Technion Institute of TechnologyHaifaIsrael

Personalised recommendations