Pab Tauschmatrix Zeile/Spalte a,b
An = Pivotelement ann betragsgrößtes Element
A: (a23 Pivot ==> a11)
A1:=P12 A P13
\(\small L1 \, := \, \left(\begin{array}{rrrr}1&0&0&0\\\frac{1}{4}&1&0&0\\-\frac{1}{2}&0&1&0\\0&0&0&1\\\end{array}\right)\) Erste Spalte nullen
A2: L1 A1 (a44 Pivot ==> a22)
A2:=P24 L1 P12 A P13 P24
\(\small A2 \, := \, \left(\begin{array}{rrrr}-4&1&-1&0\\0&-3&0&-2\\0&-\frac{1}{2}&-\frac{3}{2}&1\\0&-\frac{7}{4}&-\frac{1}{4}&-2\\\end{array}\right)\)
\(\small L2 \, := \, \left(\begin{array}{rrrr}1&0&0&0\\0&1&0&0\\0&\frac{1}{-6}&1&0\\0&-\frac{7}{12}&0&1\\\end{array}\right)\) 2.Spalte nullen
A3: L2 A2 (a33 Pivot)
A3:=L2 P24 L1 P12 A P13 P24
\(\small A3 \, := \, \left(\begin{array}{rrrr}-4&1&-1&0\\0&-3&0&-2\\0&0&-\frac{3}{2}&\frac{4}{3}\\0&0&-\frac{1}{4}&-\frac{5}{6}\\\end{array}\right)\)
\(\small L3 \, := \, \left(\begin{array}{rrrr}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&\frac{1}{-6}&1\\\end{array}\right)\) 3.Spalte nullen
R:=L3 L2 P24 L1 P12 A P13 P24
\(\small R \, := \, \left(\begin{array}{rrrr}-4&1&-1&0\\0&-3&0&-2\\0&0&-\frac{3}{2}&\frac{4}{3}\\0&0&0&-\frac{19}{18}\\\end{array}\right)\)
Abgleich Zeilen/Spaltentausch
R=(L3 L2 P24 L1 P24) P24 P12 A P13 P24
L:=(L3 L2 P24 L1 P24)^-1
\(\small L \, := \, \left(\begin{array}{rrrr}1&0&0&0\\0&1&0&0\\\frac{1}{2}&\frac{1}{6}&1&0\\-\frac{1}{4}&\frac{7}{12}&\frac{1}{6}&1\\\end{array}\right)\)
L R = (P24 P12 A P13 P24)