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Linear Algebra Ax=b

  1. Oct 2, 2015 #1
    1. The problem statement, all variables and given/known data
    Construct a 3x3 matrix A and vectors b and c in R^3 so that Ax=b has a solution but Ax=c

    2. Relevant equations


    3. The attempt at a solution
    So I don't know where to start. I am not sure if the problem is asking me to create a matrix with real numbers or variables. What I do know is that Ax=b has a solution if each row has a pivot , except the last column. So How would I use this to answer the question?
     
  2. jcsd
  3. Oct 2, 2015 #2

    andrewkirk

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    You left off a "doesn't" at the end of the question.

    Taking that as read, the matrix has to be singular, otherwise we can just left-multiply both sides by ##A^{-1}## to find solutions for both equations.

    What is the simplest, most monotonous, singular, 3 x 3 matrix you can think of?

    If you call that matrix A, what is the only vector b for which A x = b will have a solution x?

    I suspect that may not be the matrix they are looking for, but that's the simplest and most natural answer to the question as posed.
     
  4. Oct 2, 2015 #3
    Ok thank you for your help
     
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