LineareAlgebra.Aufgaben01 History
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Aufgabe 4 Gegeben sind folgende Matrizen (bzw{.} Vektoren):
Aufgabe 4 Gegeben sind folgende Matrizen:
3x-y+z+u & = & -7
x+2y-z+2u & = & -4
x-y-z-u & = & -1
2x+y+2z+u & =&-1
\end{eqnarray*}
3x-y+z+u & = & -7 \\ x+2y-z+2u & = & -4\\ x-y-z-u & = & -1 \\ 2x+y+2z+u & =&-1 \end{eqnarray*}
Aufgabe 6 Löse das folgende Gleichungssystem mit Hilfe des Gauß-Algorithmus.
$$
\begin{eqnarray*}
3x-y+z+u & = & -7
x+2y-z+2u & = & -4
x-y-z-u & = & -1
2x+y+2z+u & =&-1
\end{eqnarray*}
$$
2x+4z & = & 1 + y
-3x+2y & = & 3
2y & = & 2+6z
\end{array}
2x+4z & = & 1 + y \\ -3x+2y & = & 3\\ 2y & = & 2+6z \end{array}
Aufgabe 5 Stelle das lineare Gleichungssystem in Matrixschreibweise dar und löse es. Die benötigte inverse Matrix findet sich unter den vier angegebenen.
$$
\begin{array}{rcl}
2x+4z & = & 1 + y
-3x+2y & = & 3
2y & = & 2+6z
\end{array}
$$
$$ \scriptsize\frac{1}{30}\cdot\left(\begin{array}{ccc}8 &-2 & 8\\ 18 & 12 & 12 \\ 6 & 2 & -1\end{array}\right)\qquad\quad \frac{1}{30}\cdot\left(\begin{array}{ccc}12 &-2 & 8\\ 6 & 4 & 4 \\ 6 & 4 & -1\end{array}\right)\qquad\quad \frac{1}{30}\cdot\left(\begin{array}{ccc}12 &-2 & 8\\ 18 & 12 & 12 \\ 6 & 4 & -1\end{array}\right)\qquad\quad \frac{1}{30}\cdot\left(\begin{array}{ccc}12 &-2 & -8\\ 8 & 12 & 12 \\ 6 & 4 & -1\end{array}\right) $$
E=\left(\begin{array}{cc}-1 &-4 \\ 3 & 2 \end{array}\right),\quad
F=\left(\begin{array}{c}-1 \\ 2 \\ 3 \end{array}\right),\quad
G=\left(\begin{array}{cc}5 & 7 \end{array}\right)
E=\left(\begin{array}{cc}-1 &-4 \\ 3 & 2 \end{array}\right),\quad F=\left(\begin{array}{c}-1 \\ 2 \\ 3 \end{array}\right),\quad G=\left(\begin{array}{cc}5 & 7 \end{array}\right)
A=\left(\begin{array}{cc}2 &3 \\ -5 & 1 \end{array}\right),\quad
B=\left(\begin{array}{c}-3 \\-2\end{array}\right),\quad
C=\left(\begin{array}{ccc}-1 &4 &-2 \\ 2 & 3&5 \end{array}\right),\quad
D=\left(\begin{array}{cc}3 &1 \\ -2 & 4 \\1&-3 \end{array}\right)
A=\left(\begin{array}{cc}2 &3 \\ -5 & 1 \end{array}\right),\quad B=\left(\begin{array}{c}-3 \\-2\end{array}\right),\quad C=\left(\begin{array}{ccc}-1 &4 &-2 \\ 2 & 3&5 \end{array}\right),\quad D=\left(\begin{array}{cc}3 &1 \\ -2 & 4 \\1&-3 \end{array}\right)
Aufgabe 4 Gegeben sind folgende Matrizen (bzw{.} Vektoren): $$ A=\left(\begin{array}{cc}2 &3 \\ -5 & 1 \end{array}\right),\quad
B=\left(\begin{array}{c}-3 \\-2\end{array}\right),\quad
C=\left(\begin{array}{ccc}-1 &4 &-2 \\ 2 & 3&5 \end{array}\right),\quad
D=\left(\begin{array}{cc}3 &1 \\ -2 & 4 \\1&-3 \end{array}\right)
$$ $$ E=\left(\begin{array}{cc}-1 &-4 \\ 3 & 2 \end{array}\right),\quad
F=\left(\begin{array}{c}-1 \\ 2 \\ 3 \end{array}\right),\quad
G=\left(\begin{array}{cc}5 & 7 \end{array}\right)
$$
- Welche der angegebenen Produkte lassen sich bilden? Warum? AB,BA,AE,EA,CD,DC,GA,GB,BG,FC,CF,ED,DE
- Betrachte nur B, C und G. Berechne untereinander alle möglichen Produkte.
- Formuliere eine Bedingung dafür, wann zwei Matrizen miteinander multipliziert werden können.
Aufgaben01>>
Aufgaben01 >>
Aufgaben01>>
Aufgaben01 >>
\mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right) \quad \mbox{d)}\; A= \left( \begin{array}{cc} a & 0 \\ 1 & b\end{array} \right) \quad \mbox{e)}\; A= \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0&0&1\end{array} \right)
\mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right) \quad \mbox{d)}\; A= \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0&0&1\end{array} \right)
\mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right) \quad \mbox{d)}\; A= \left( \begin{array}{cc} a & 0 \\ 1 & b\end{array} \right) \quad \mbox{e)}\; A= \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0&0&1\end{array}
\mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right) \quad \mbox{d)}\; A= \left( \begin{array}{cc} a & 0 \\ 1 & b\end{array} \right) \quad \mbox{e)}\; A= \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0&0&1\end{array} \right)
\mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right)
\mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right) \quad \mbox{d)}\; A= \left( \begin{array}{cc} a & 0 \\ 1 & b\end{array} \right) \quad \mbox{e)}\; A= \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0&0&1\end{array}
$$
$$
Aufgabe 3 Berechne jeweils A^2, A^3 und A^4. $$ \mbox{a)}\; A= \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0&0&3\end{array} \right) \quad \mbox{b)}\; A= \left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 2 & 0 \\ 3&0&0\end{array} \right) \quad \mbox{c)}\; A= \left( \begin{array}{cc} a & 1 \\ 0 & b\end{array} \right) $$
\mbox{d)}\; & \left( \begin{array}{ccc} 2 & -1 & 12 \end{array} \right)\cdot \left( \begin{array}{c} 6\\ 0 \\ -3 \end{array} \right) \quad & \mbox{e)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \end{array}
\mbox{d)}\; & \left( \begin{array}{ccc} 2 & -1 & 12 \end{array} \right)\cdot \left( \begin{array}{c} 6\\ 0 \\ -3 \end{array} \right) \quad & \mbox{e)}\; & \left( \begin{array}{cc} 0,3 & -2 \\ 0,7 & 0,1 \end{array} \right)\cdot \left( \begin{array}{c} 10\\ 5 \end{array} \right) \quad & \mbox{f)}\; & \left( \begin{array}{cc} \sqrt{2} & -\sqrt{3}\\ -\sqrt{2} & \sqrt{3} \end{array} \right)\cdot \left( \begin{array}{c} \sqrt{2}\\ \sqrt{3} \end{array} \right) \end{array}
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\ \mbox{ }
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \end{array}
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\ \mbox{d)}\; & \left( \begin{array}{ccc} 2 & -1 & 12 \end{array} \right)\cdot \left( \begin{array}{c} 6\\ 0 \\ -3 \end{array} \right) \quad & \mbox{e)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \end{array}
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\\vspace{1em} \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\ \mbox{ } \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\ \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\\vspace{1em} \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\ \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \\
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \end{array}
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right)
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \end{array}
\begin{array}{llll} \mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0 & 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad \end{array}
\begin{array}{llllll} \mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad & \mbox{c)}\; & \left( \begin{array}{cc} 7 & -7\\ 3 & 2 \end{array} \right)\cdot \left( \begin{array}{c} -2\\ 2 \end{array} \right) \end{array}
\mabox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0 & 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad \end{array}
\mbox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0 & 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad \end{array}
Aufgabe 1 Bilde für die folgenden Matrizen alle möglichen Matrixprodukte:
Übungsaufgaben: Rechnen mit Matrizen
Aufgabe1 Berechne. $$ \begin{array}{llll} \mabox{a)}\; & \left( \begin{array}{ccc} -3 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & -2 & 3 \end{array} \right)\cdot \left( \begin{array}{c} 1\\ 2 \\ 3 \end{array} \right) \quad & \mbox{b)}\; & \left( \begin{array}{cc} 1 & -1 \\ 3 & 0 \\ 0 & 0,5 & 0,3 \end{array} \right)\cdot \left( \begin{array}{c} 5\\ 5 \end{array} \right) \quad \end{array} $$
Aufgabe 2 Bilde für die folgenden Matrizen alle möglichen Matrixprodukte:
Bilde für die folgenden Matrizen alle möglichen Matrixprodukte:
Aufgabe 1 Bilde für die folgenden Matrizen alle möglichen Matrixprodukte:
$$ A= \left( \begin{array}{ccc} 1 & 4 & -2
3 & 5 & 0 \end{array} \right) \; ,\;
B= \left( \begin{array}{cc} 3 & -1
0 & 2 \end{array} \right) \; ,\;
$$ A= \left( \begin{array}{ccc} 1 & 4 & -2 \\ 3 & 5 & 0 \end{array} \right) \; ,\; B= \left( \begin{array}{cc} 3 & -1 \\ 0 & 2 \end{array} \right) \; ,\;
$$ A= \left( \begin{array}{ccc} 1 & 4 & -2 \\
$$ A= \left( \begin{array}{ccc} 1 & 4 & -2 \\
Bilde für die folgenden Matrizen alle möglichen Matrixprodukte:
$$
A= \left( \begin{array}{ccc} 1 & 4 & -2
3 & 5 & 0 \end{array} \right) \; ,\;
B= \left( \begin{array}{cc} 3 & -1
0 & 2 \end{array} \right) \; ,\;
C=\left( \begin{array}{ccc} 4 & 1 & 8 \\ 5 & 7 & 0 \\ 0 & 0 & 3 \end{array} \right) \; ,\;D= \left( \begin{array}{c} -2 \\ 8 \\ 1 \end{array} \right) \; ,\;
E = \left( \begin{array}{cc} 3 & 2 \end{array} \right) $$