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Linear Algebra Problems

  1. Mar 17, 2013 #1
    Linear Algebra Problems
    Are there any resources consisting of a collection of problems on linear algebra for students to practice? I am looking for good interesting problems which test students’ understanding. These questions or examples should be for teaching rather than just testing. The level of difficulty is first year undergraduate.
  2. jcsd
  3. Mar 17, 2013 #2
  4. Mar 17, 2013 #3
    Let me know if you find any matqkks. I too am interested.
  5. Mar 22, 2013 #4
    Last edited by a moderator: May 6, 2017
  6. Sep 25, 2013 #5
    I am looking for help in this question."Rather than using the standard definitions of addition and scalar multiplication in R^3, suppose the operation is define as follows: (c1,y1,z1,) + (x2,y2,z2) = (x1+x2+1,y1+y2+1,z1+z2+1)

    c(x,y,z) = (cx,cy,cz)
    With this new definitions, is a vector space?
    Justify your answers
  7. Sep 30, 2013 #6


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    Determine whether or not this addition (the scalar multiplication defined is just the usual one on [itex]R^3[/itex]) has the properties required for addition in a vector space:
    1) u+ v= v+ u (commutativity)
    2) (u+ v)+ w= u+ (v+ w) (associativity)
    3) There exist a specific vector, O, such that v+ O= O+ v= v for any vector v (O is NOT necessarily (0, 0, 0)).
    4) For any vector v, there exist a vector, u, such that v+ u= u+ v= O.
    5) For any number, a, and vectors u and v, a(u+ v)= au+ av. (Distributive)
  8. Sep 30, 2013 #7
    The examples sheets for the Cambridge Linear Algebra course contain some excellent questions. They can be found here.

    In particular, the "Preliminary example sheet" (essentially a revision sheet) might be just what you seek.
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