rozwiazanie bazowe ukladow rownan

[studentka87]

Wyznaczyć rozwiązanie ogólne i wszystkie rozwiązania bazowe poniższych układów równań

a)
\(\displaystyle{ x_{1}}\) + \(\displaystyle{ x_{2}}\) + \(\displaystyle{ 2x_{3}}\) = 10
\(\displaystyle{ -x_{1}}\) + \(\displaystyle{ 2x_{2}}\) - \(\displaystyle{ 4x_{3}}\) = 20

b)
\(\displaystyle{ x_{1}}\) - \(\displaystyle{ 2x_{2}}\) + \(\displaystyle{ 3x_{3}}\) - \(\displaystyle{ x_{4}}\) = 1
\(\displaystyle{ 2x_{1}}\) + \(\displaystyle{ x_{2}}\) + \(\displaystyle{ x_{3}}\) - \(\displaystyle{ 3x_{4}}\) = 4
c)
\(\displaystyle{ 3x_{1}}\) + \(\displaystyle{ x_{2}}\) - \(\displaystyle{ x_{3}}\) ................. = 30
\(\displaystyle{ -x_{1}}\) ................. ..... + \(\displaystyle{ 3x_{3}}\) + \(\displaystyle{ x_{4}}\) =10
\(\displaystyle{ x_{1}}\) ...................... - \(\displaystyle{ x_{3}}\) ................ \(\displaystyle{ -x_{5}}\)=0
d)
\(\displaystyle{ 2x_{1}}\) + \(\displaystyle{ 2x_{2}}\) - \(\displaystyle{ x_{3}}\) - \(\displaystyle{ x_{4}}\) = 1
\(\displaystyle{ x_{1}}\) + \(\displaystyle{ 2x_{2}}\) - \(\displaystyle{ x_{3}}\) .................. = -2
\(\displaystyle{ 3x_{1}}\) + \(\displaystyle{ 3x_{2}}\) - \(\displaystyle{ x_{3}}\) - \(\displaystyle{ x_{4}}\) = -6

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