Lignings fejl?

Jeg har regnet denne ligning


x(1) + 2x(2) + x(3) + x(4) = 0

x(1) + a+2x(2) + x(3) + x(5) = 0

x(1) + 2x(2) + a+2x(3) + a = 1

MEN nu har jeg fundet ud af at jeg har levet en fejl, da ligningen hed

x(1) + 2x(2) + x(3) + x(4) = 0

x(1) + (a+2)x(2) + x(3) + x(5) = 0

x(1) + 2x(2) + (a+2)x(3) + a = 1

Ka jeg stadig bruge mine resultater??? hvad gør jeg, er på bar bund?



x(1) x(2) x(3) x(4) x(5) a

1 2 1 1 0 0 | 0

1 2 1 0 1 1 | 0

1 2 2 0 0 1 | 1



1 2 1 1 0 0 | 0

0 0 0 -1 1 1 | 0 L2 - L1

0 0 1 -1 0 1 | 1 L3 - L1



1 2 1 1 0 0 | 0

0 0 0 -1 1 1 | 0

0 0 1 0 -1 0 | 1 L3 - L2



x(1) + 2x(2) + x(3) + x(4) = 0

- x(4) + x(5) = 0

x(3) - x(5) = 1



==> x(3) = x(5) + 1

x(5) = x(4) - a

x(4) = x(5) + a



so x(1) + 2x(2) + x(3) + x(4) = 0

==> x(1) + 2x(2) + (x(5) + 1) + (x(5) + a) = 0

==> x(1) + 2x(2) + 2x(5) + 1 + a

==> 2x(5) = - ( x(1) + 2x(2) + a +1 )

==> x(5) = - ( x(1) + 2x(2) + a +1 ) / 2




x(3) = x(5) + 1

==> x(3) = (- ( x(1) + 2x(2) + a + 1 ) / 2) + 1

==> x(3) = (- ( x(1) + 2x(2) + a + 1 ) / 2) + 2/2

==> x(3) = (- ( x(1) + 2x(2) + a + 1 - 2 ) / 2)

==> x(3) = - ( x(1) + 2x(2) + a - 1 ) / 2



x(4) = x(5) + a

==> x(4) = (- ( x(1) + 2x(2) + a + 1 ) / 2) + a

==> x(4) = (- ( x(1) + 2x(2) + a + 1 ) / 2) + 2a/2

==> x(4) = (- x(1) - 2x(2) + 2a - a - 1 ) / 2

==> x(4) = (- x(1) - 2x(2) + a - 1 ) / 2




{x(1) € R ; x(2) € R ; a € R ; x(5) = - ( x(1) + 2x(2) + a +1 ) / 2 ; x(3) = - ( x(1) + 2x(2) + a - 1 ) / 2 ; x(4) = (- x(1) - 2x(2) + a - 1 ) / 2 }