Finite Mathematik Beispiele

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ 1 & 0 & 1 & - 1 \end{array}]$

Schritt 1

Perform the row operation $R_{3} = R_{3} - R_{1}$ to make the entry at $3, 1$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.1

Perform the row operation $R_{3} = R_{3} - R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ 1 - 1 & 0 + 1 & 1 - 0 & - 1 - 1 \end{array}]$

Schritt 1.2

Vereinfache $R_{3}$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ 0 & 1 & 1 & - 2 \end{array}]$

Schritt 2

Perform the row operation $R_{3} = R_{3} - R_{2}$ to make the entry at $3, 2$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 2.1

Perform the row operation $R_{3} = R_{3} - R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ 0 - 0 & 1 - 1 & 1 + 1 & - 2 - 6 \end{array}]$

Schritt 2.2

Vereinfache $R_{3}$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ 0 & 0 & 2 & - 8 \end{array}]$

Schritt 3

Multiply each element of $R_{3}$ by $\frac{1}{2}$ to make the entry at $3, 3$ a $1$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 3.1

Multiply each element of $R_{3}$ by $\frac{1}{2}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ \frac{0}{2} & \frac{0}{2} & \frac{2}{2} & \frac{- 8}{2} \end{array}]$

Schritt 3.2

Vereinfache $R_{3}$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & - 1 & 6 \\ 0 & 0 & 1 & - 4 \end{array}]$

Schritt 4

Perform the row operation $R_{2} = R_{2} + R_{3}$ to make the entry at $2, 3$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.1

Perform the row operation $R_{2} = R_{2} + R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 + 0 & 1 + 0 & - 1 + 1 \cdot 1 & 6 - 4 \\ 0 & 0 & 1 & - 4 \end{array}]$

Schritt 4.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - 1 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & - 4 \end{array}]$

Schritt 5

Perform the row operation $R_{1} = R_{1} + R_{2}$ to make the entry at $1, 2$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.1

Perform the row operation $R_{1} = R_{1} + R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + 0 & - 1 + 1 \cdot 1 & 0 + 0 & 1 + 1 \cdot 2 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & - 4 \end{array}]$

Schritt 5.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 3 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & - 4 \end{array}]$