Mixing
why can we tackle a matrix with linearly dependent rows while driving artificial variables out of the basis?
$begingroup$
in introduction to linear programming, section 3.5 driving artificial variables out of the basis, the authors consider the case where that when trying to drive the lth basic variable (which is artificial), we find out that the lth row of $B^{-1}A$ is zero, which means that A has linearly dependent rows (last paragraph of page 113)
How is that possible? I thought that our assumption is that A has full rank! and that we test for that before the optimization...
Thanks!
related to why in Phase I of the simplex method, if artificial variable become nonbasic, it never become basic?
optimization linear-programming simplex
asked Jan 14 at 21:16
ihadannyihadanny
1257
$endgroup$
add a comment |
$begingroup$
in introduction to linear programming, section 3.5 driving artificial variables out of the basis, the authors consider the case where that when trying to drive the lth basic variable (which is artificial), we find out that the lth row of $B^{-1}A$ is zero, which means that A has linearly dependent rows (last paragraph of page 113)
How is that possible? I thought that our assumption is that A has full rank! and that we test for that before the optimization...
Thanks!
related to why in Phase I of the simplex method, if artificial variable become nonbasic, it never become basic?
optimization linear-programming simplex
asked Jan 14 at 21:16
ihadannyihadanny
1257
$endgroup$
$begingroup$
Please specify where you´ve read that the lth row is $0$.
$endgroup$
– callculus
Jan 15 at 6:26
$begingroup$
@callculus - edited
$endgroup$
– ihadanny
Jan 15 at 12:27
add a comment |
$begingroup$
in introduction to linear programming, section 3.5 driving artificial variables out of the basis, the authors consider the case where that when trying to drive the lth basic variable (which is artificial), we find out that the lth row of $B^{-1}A$ is zero, which means that A has linearly dependent rows (last paragraph of page 113)
How is that possible? I thought that our assumption is that A has full rank! and that we test for that before the optimization...
Thanks!
related to why in Phase I of the simplex method, if artificial variable become nonbasic, it never become basic?
optimization linear-programming simplex
asked Jan 14 at 21:16
ihadannyihadanny
1257
$endgroup$
in introduction to linear programming, section 3.5 driving artificial variables out of the basis, the authors consider the case where that when trying to drive the lth basic variable (which is artificial), we find out that the lth row of $B^{-1}A$ is zero, which means that A has linearly dependent rows (last paragraph of page 113)
How is that possible? I thought that our assumption is that A has full rank! and that we test for that before the optimization...
Thanks!
related to why in Phase I of the simplex method, if artificial variable become nonbasic, it never become basic?
optimization linear-programming simplex
optimization linear-programming simplex
asked Jan 14 at 21:16
ihadannyihadanny
1257
asked Jan 14 at 21:16
ihadannyihadanny
1257
edited Jan 15 at 12:27
ihadanny
asked Jan 14 at 21:16
ihadannyihadanny
1257
asked Jan 14 at 21:16
ihadannyihadanny
1257
asked Jan 14 at 21:16
ihadannyihadanny
1257
1257
$begingroup$
Please specify where you´ve read that the lth row is $0$.
$endgroup$
– callculus
Jan 15 at 6:26
$begingroup$
@callculus - edited
$endgroup$
– ihadanny
Jan 15 at 12:27
add a comment |
$begingroup$
Please specify where you´ve read that the lth row is $0$.
$endgroup$
– callculus
Jan 15 at 6:26
$begingroup$
@callculus - edited
$endgroup$
– ihadanny
Jan 15 at 12:27
$begingroup$
Please specify where you´ve read that the lth row is $0$.
$endgroup$
– callculus
Jan 15 at 6:26
$begingroup$
Please specify where you´ve read that the lth row is $0$.
$endgroup$
– callculus
Jan 15 at 6:26
$begingroup$
@callculus - edited
$endgroup$
– ihadanny
Jan 15 at 12:27
$begingroup$
@callculus - edited
$endgroup$
– ihadanny
Jan 15 at 12:27
add a comment |
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$begingroup$
Please specify where you´ve read that the lth row is $0$.
$endgroup$
– callculus
Jan 15 at 6:26
$begingroup$
@callculus - edited
$endgroup$
– ihadanny
Jan 15 at 12:27