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--- lehrkraefte:blc:linalg20:start [2020/11/17 08:44]
Ivo Blöchliger
+++ lehrkraefte:blc:linalg20:start [2020/11/17 08:57]
Ivo Blöchliger
@@ Line 17: / Line 17: @@
 </PRELOAD>
+Hinweis: Die Aufgaben sind automatisch generiert und ändern sich beim Neu-Laden der Seite.
 ==== Matrix-Vektor Multiplikation ====
 Berechnen Sie:<JS>miniAufgabe("#exomatrixvectormultiplikation","#solmatrixvectormultiplikation",
@@ Line 29: / Line 30: @@
 <HTML>
 <div id="solmatrixvectormultiplikation"></div>
+</HTML>
+</hidden>
+Berechnen Sie:<JS>miniAufgabe("#exomatrixvectormultiplikation2D","#solmatrixvectormultiplikation2D",
+[["$\\begin{pmatrix}1 & 1 & 6\\\\\n-1 & 0 & -4\\\\\n-6 & 3 & -1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n-2\\\\\n4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}1 & 1 & 6\\\\\n-1 & 0 & -4\\\\\n-6 & 3 & -1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n-2\\\\\n4\\\\\n\\end{pmatrix} = \\begin{pmatrix}28\\\\\n-22\\\\\n-46\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-4 & -3 & 2\\\\\n3 & 4 & 3\\\\\n-1 & -5 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}3\\\\\n-1\\\\\n3\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-4 & -3 & 2\\\\\n3 & 4 & 3\\\\\n-1 & -5 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}3\\\\\n-1\\\\\n3\\\\\n\\end{pmatrix} = \\begin{pmatrix}-3\\\\\n14\\\\\n2\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-2 & 0 & -1\\\\\n3 & -1 & 2\\\\\n5 & 1 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-5\\\\\n0\\\\\n1\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-2 & 0 & -1\\\\\n3 & -1 & 2\\\\\n5 & 1 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-5\\\\\n0\\\\\n1\\\\\n\\end{pmatrix} = \\begin{pmatrix}9\\\\\n-13\\\\\n-31\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-3 & -1 & 1\\\\\n2 & 5 & -6\\\\\n3 & -2 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}0\\\\\n2\\\\\n2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-3 & -1 & 1\\\\\n2 & 5 & -6\\\\\n3 & -2 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}0\\\\\n2\\\\\n2\\\\\n\\end{pmatrix} = \\begin{pmatrix}0\\\\\n-2\\\\\n-4\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}0 & 3 & -1\\\\\n-1 & -1 & 4\\\\\n2 & -1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}3\\\\\n5\\\\\n-4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}0 & 3 & -1\\\\\n-1 & -1 & 4\\\\\n2 & -1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}3\\\\\n5\\\\\n-4\\\\\n\\end{pmatrix} = \\begin{pmatrix}19\\\\\n-24\\\\\n-3\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}5 & 3 & 5\\\\\n-2 & -3 & 1\\\\\n4 & -1 & 2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-5\\\\\n-1\\\\\n-6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}5 & 3 & 5\\\\\n-2 & -3 & 1\\\\\n4 & -1 & 2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-5\\\\\n-1\\\\\n-6\\\\\n\\end{pmatrix} = \\begin{pmatrix}-58\\\\\n7\\\\\n-31\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}6 & 5 & 1\\\\\n-2 & -3 & 3\\\\\n-4 & -2 & 5\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-6\\\\\n-1\\\\\n6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}6 & 5 & 1\\\\\n-2 & -3 & 3\\\\\n-4 & -2 & 5\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-6\\\\\n-1\\\\\n6\\\\\n\\end{pmatrix} = \\begin{pmatrix}-35\\\\\n33\\\\\n56\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-6 & -1 & 0\\\\\n-6 & -4 & -6\\\\\n1 & 1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-6\\\\\n3\\\\\n2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-6 & -1 & 0\\\\\n-6 & -4 & -6\\\\\n1 & 1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-6\\\\\n3\\\\\n2\\\\\n\\end{pmatrix} = \\begin{pmatrix}33\\\\\n12\\\\\n-1\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}4 & 3 & -3\\\\\n5 & -6 & 1\\\\\n-3 & 4 & -3\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n-3\\\\\n-6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}4 & 3 & -3\\\\\n5 & -6 & 1\\\\\n-3 & 4 & -3\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n-3\\\\\n-6\\\\\n\\end{pmatrix} = \\begin{pmatrix}1\\\\\n2\\\\\n12\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-3 & 2 & -3\\\\\n2 & 5 & -6\\\\\n0 & 0 & 3\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}3\\\\\n-3\\\\\n-1\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-3 & 2 & -3\\\\\n2 & 5 & -6\\\\\n0 & 0 & 3\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}3\\\\\n-3\\\\\n-1\\\\\n\\end{pmatrix} = \\begin{pmatrix}-12\\\\\n-3\\\\\n-3\\\\\n\\end{pmatrix}$"]],
+" <br> ");
+</JS>
+<HTML>
+<div id="exomatrixvectormultiplikation2D"></div>
+</HTML>
+<hidden Lösungen>
+<HTML>
+<div id="solmatrixvectormultiplikation2D"></div>
+</HTML>
+</hidden>
+==== Matrix-Matrix Multiplikation ====
+Berechnen Sie:<JS>miniAufgabe("#exomatrixmatrixmultiplikation3D","#solmatrixmatrixmultiplikation3D",
+[["$\\begin{pmatrix}-4 & -1\\\\\n-3 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n-6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-4 & -1\\\\\n-3 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n-6\\\\\n\\end{pmatrix} = \\begin{pmatrix}-18\\\\\n-18\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-2 & 1\\\\\n-6 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-2 & 1\\\\\n-6 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n2\\\\\n\\end{pmatrix} = \\begin{pmatrix}0\\\\\n-4\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}0 & 0\\\\\n-1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}5\\\\\n-2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}0 & 0\\\\\n-1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}5\\\\\n-2\\\\\n\\end{pmatrix} = \\begin{pmatrix}0\\\\\n-7\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}2 & 5\\\\\n-3 & -5\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-4\\\\\n-4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}2 & 5\\\\\n-3 & -5\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-4\\\\\n-4\\\\\n\\end{pmatrix} = \\begin{pmatrix}-28\\\\\n32\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}3 & 5\\\\\n0 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}3 & 5\\\\\n0 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n6\\\\\n\\end{pmatrix} = \\begin{pmatrix}33\\\\\n0\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}3 & 2\\\\\n-1 & 4\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}3 & 2\\\\\n-1 & 4\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n6\\\\\n\\end{pmatrix} = \\begin{pmatrix}6\\\\\n26\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}3 & -2\\\\\n4 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}3 & -2\\\\\n4 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n4\\\\\n\\end{pmatrix} = \\begin{pmatrix}10\\\\\n0\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}5 & -4\\\\\n-5 & 2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}5 & -4\\\\\n-5 & 2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n2\\\\\n\\end{pmatrix} = \\begin{pmatrix}-18\\\\\n14\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-1 & -4\\\\\n5 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n-4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-1 & -4\\\\\n5 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n-4\\\\\n\\end{pmatrix} = \\begin{pmatrix}18\\\\\n14\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}4 & 3\\\\\n5 & 4\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-5\\\\\n-3\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}4 & 3\\\\\n5 & 4\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-5\\\\\n-3\\\\\n\\end{pmatrix} = \\begin{pmatrix}-29\\\\\n-37\\\\\n\\end{pmatrix}$"]],
+" <br> ");
+</JS>
+<HTML>
+<div id="exomatrixmatrixmultiplikation3D"></div>
+</HTML>
+<hidden Lösungen>
+<HTML>
+<div id="solmatrixmatrixmultiplikation3D"></div>
+</HTML>
+</hidden>
+Berechnen Sie:<JS>miniAufgabe("#exomatrixmatrixmultiplikation4D","#solmatrixmatrixmultiplikation4D",
+[["$\\begin{pmatrix}1 & 0 & -4\\\\\n4 & 3 & 5\\\\\n3 & 0 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-4\\\\\n-3\\\\\n-6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}1 & 0 & -4\\\\\n4 & 3 & 5\\\\\n3 & 0 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-4\\\\\n-3\\\\\n-6\\\\\n\\end{pmatrix} = \\begin{pmatrix}20\\\\\n-55\\\\\n-18\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-3 & -5 & -3\\\\\n0 & -5 & 0\\\\\n2 & 5 & -2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-3\\\\\n1\\\\\n4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-3 & -5 & -3\\\\\n0 & -5 & 0\\\\\n2 & 5 & -2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-3\\\\\n1\\\\\n4\\\\\n\\end{pmatrix} = \\begin{pmatrix}-8\\\\\n-5\\\\\n-9\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}2 & -6 & 1\\\\\n-3 & -1 & 4\\\\\n6 & -5 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}0\\\\\n2\\\\\n-5\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}2 & -6 & 1\\\\\n-3 & -1 & 4\\\\\n6 & -5 & -6\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}0\\\\\n2\\\\\n-5\\\\\n\\end{pmatrix} = \\begin{pmatrix}-17\\\\\n-22\\\\\n20\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}6 & 4 & 2\\\\\n-5 & -4 & 1\\\\\n0 & -6 & -2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n4\\\\\n2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}6 & 4 & 2\\\\\n-5 & -4 & 1\\\\\n0 & -6 & -2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-2\\\\\n4\\\\\n2\\\\\n\\end{pmatrix} = \\begin{pmatrix}8\\\\\n-4\\\\\n-28\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-3 & -2 & 4\\\\\n-1 & 6 & -1\\\\\n6 & -4 & -2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-3\\\\\n5\\\\\n-2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-3 & -2 & 4\\\\\n-1 & 6 & -1\\\\\n6 & -4 & -2\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}-3\\\\\n5\\\\\n-2\\\\\n\\end{pmatrix} = \\begin{pmatrix}-9\\\\\n35\\\\\n-34\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-3 & 2 & 3\\\\\n-2 & 3 & 6\\\\\n-2 & 3 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n2\\\\\n6\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-3 & 2 & 3\\\\\n-2 & 3 & 6\\\\\n-2 & 3 & 0\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n2\\\\\n6\\\\\n\\end{pmatrix} = \\begin{pmatrix}4\\\\\n30\\\\\n-6\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-6 & -1 & 6\\\\\n-2 & 1 & 4\\\\\n2 & -6 & -4\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n-2\\\\\n-5\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-6 & -1 & 6\\\\\n-2 & 1 & 4\\\\\n2 & -6 & -4\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n-2\\\\\n-5\\\\\n\\end{pmatrix} = \\begin{pmatrix}-34\\\\\n-24\\\\\n34\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}2 & 6 & -3\\\\\n4 & 2 & -6\\\\\n-3 & -1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}2\\\\\n-3\\\\\n0\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}2 & 6 & -3\\\\\n4 & 2 & -6\\\\\n-3 & -1 & 1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}2\\\\\n-3\\\\\n0\\\\\n\\end{pmatrix} = \\begin{pmatrix}-14\\\\\n2\\\\\n-3\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-1 & 6 & -6\\\\\n0 & -3 & 5\\\\\n6 & -6 & -1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n6\\\\\n2\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-1 & 6 & -6\\\\\n0 & -3 & 5\\\\\n6 & -6 & -1\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}6\\\\\n6\\\\\n2\\\\\n\\end{pmatrix} = \\begin{pmatrix}18\\\\\n-8\\\\\n-2\\\\\n\\end{pmatrix}$"], ["$\\begin{pmatrix}-3 & -5 & 2\\\\\n-3 & -2 & -5\\\\\n-2 & -4 & -3\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n5\\\\\n4\\\\\n\\end{pmatrix}$", "$\\begin{pmatrix}-3 & -5 & 2\\\\\n-3 & -2 & -5\\\\\n-2 & -4 & -3\\\\\n\\end{pmatrix} \\cdot \\begin{pmatrix}1\\\\\n5\\\\\n4\\\\\n\\end{pmatrix} = \\begin{pmatrix}-20\\\\\n-33\\\\\n-34\\\\\n\\end{pmatrix}$"]],
+" <br> ");
+</JS>
+<HTML>
+<div id="exomatrixmatrixmultiplikation4D"></div>
+</HTML>
+<hidden Lösungen>
+<HTML>
+<div id="solmatrixmatrixmultiplikation4D"></div>
 </HTML>
 </hidden>