For a non homogenous system of equation Ax=b can we say something about the relation between dimension of...












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For a homogenous system of linear equation we know the dimension of the solution space is nulity of A, but what can we say the dimension of the solution space of the non homogeneous system in terms of of rank A? Since the system is non homogenous, so I think we cant relate directly the dimension of the solution space and nulity of A.
Please tell me if I'm going wrong somewhere.
Thanks in advane.






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    $begingroup$


    For a homogenous system of linear equation we know the dimension of the solution space is nulity of A, but what can we say the dimension of the solution space of the non homogeneous system in terms of of rank A? Since the system is non homogenous, so I think we cant relate directly the dimension of the solution space and nulity of A.
    Please tell me if I'm going wrong somewhere.
    Thanks in advane.






    linear-algebra







    share|cite|improve this question









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      $begingroup$


      For a homogenous system of linear equation we know the dimension of the solution space is nulity of A, but what can we say the dimension of the solution space of the non homogeneous system in terms of of rank A? Since the system is non homogenous, so I think we cant relate directly the dimension of the solution space and nulity of A.
      Please tell me if I'm going wrong somewhere.
      Thanks in advane.






      linear-algebra







      share|cite|improve this question









      $endgroup$




      For a homogenous system of linear equation we know the dimension of the solution space is nulity of A, but what can we say the dimension of the solution space of the non homogeneous system in terms of of rank A? Since the system is non homogenous, so I think we cant relate directly the dimension of the solution space and nulity of A.
      Please tell me if I'm going wrong somewhere.
      Thanks in advane.






      linear-algebra




      linear-algebra






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      asked Jan 29 at 4:08









      user639336user639336

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