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Linear Algebra Terms T/F

  1. Jun 22, 2012 #1
    True or False Questions. I have put my answers to them but one or more is incorrect, can anybody tell me which ones?

    Note: The linear system Ax=b of m equations in n unknowns is called:

    square if m=n
    overdertermined if m>n
    undeterdetermined if m<n
    homogeneous if b= 0
    inhomogeneous b != 0
    consistent if it has a solution
    inconsistent if it does not have a solution.

    Below, we refer to Ax= b of m equations in n unknown simply as "the system". The corresponding homogeneous system is Ax=0

    Questions:

    1. The general solution of the system equals any particular solution plus the general solution of the corresponding homogeneous system. T

    2. An underdetermined system may have no solutions. T

    3. An overdetermined system may have a unique solution. T

    4. An overdetermined system may have infinitely many solutions. T

    5. An underdetermined system may not have a unique solution. F

    6. Every homogeneous system is consistent. F

    7. An overdetermined system may be consistent. T

    8. An underdetermined system may be inconsistent. T

    9. The solutions of the system form a linear space if and only if the system is homogeneous. T

    10. The null space of A is a subspace of R^n. T

    11. The column space of A is a subspace of R^m. T

    12. For a square system the column and null spaces of A may be the same. T

    13. The system is consistent if and only if b is in the column space of A. T
     
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  3. Jun 22, 2012 #2

    vela

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    It would help if you gave a brief explanation for how you reached each of these answers.
     
  4. Jun 22, 2012 #3

    SammyS

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    What vela said is a reflections of the rules for posting in the Homework help section.

    This is especially true in your case, since you posted a thread with true/false previously, and never replied to any of the help that was given.
     
  5. Jun 22, 2012 #4

    SammyS

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    temporary copy:
     
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