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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?

  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


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    Homework Helper

    just do the algebra.
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