Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear independence and dependence

  1. Feb 12, 2007 #1
    Hi everyone, having problems with this question, can anyone please help

    Question: consider a 2 x 2 matrix, can you construct a matrix whose columns are linearly dependent and whose rows are linearly independent?

    My answer is no. I cannot think of any combination that would make this true? Or is there? If so why?

    Thanks
     
  2. jcsd
  3. Feb 12, 2007 #2
    No, because having linearly dependent columns gives a singular matrix yet linearly independent rows gives a non-singular matrix.
     
  4. Feb 12, 2007 #3
    Thanks, make sense.
     
  5. Feb 12, 2007 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    just do the algebra.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?