Finite Mathematik Beispiele

$8 x - 7 y = 8$ , $16 x - 14 y = 3$

Schritt 1

Write the system as a matrix.

$[\begin{array}{c} 8 & - 7 & 8 \\ 16 & - 14 & 3 \end{array}]$

Schritt 2

Ermittele die normierte Zeilenstufenform.

Tippen, um mehr Schritte zu sehen ...

Schritt 2.1

Multiply each element of $R_{1}$ by $\frac{1}{8}$ to make the entry at $1, 1$ a $1$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 2.1.1

Multiply each element of $R_{1}$ by $\frac{1}{8}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{8}{8} & \frac{- 7}{8} & \frac{8}{8} \\ 16 & - 14 & 3 \end{array}]$

Schritt 2.1.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & 1 \\ 16 & - 14 & 3 \end{array}]$

Schritt 2.2

Perform the row operation $R_{2} = R_{2} - 16 R_{1}$ to make the entry at $2, 1$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 2.2.1

Perform the row operation $R_{2} = R_{2} - 16 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & 1 \\ 16 - 16 \cdot 1 & - 14 - 16 (- \frac{7}{8}) & 3 - 16 \cdot 1 \end{array}]$

Schritt 2.2.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & 1 \\ 0 & 0 & - 13 \end{array}]$

Schritt 2.3

Multiply each element of $R_{2}$ by $- \frac{1}{13}$ to make the entry at $2, 3$ a $1$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 2.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{13}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & 1 \\ - \frac{1}{13} \cdot 0 & - \frac{1}{13} \cdot 0 & - \frac{1}{13} \cdot - 13 \end{array}]$

Schritt 2.3.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & 1 \\ 0 & 0 & 1 \end{array}]$

Schritt 2.4

Perform the row operation $R_{1} = R_{1} - R_{2}$ to make the entry at $1, 3$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 2.4.1

Perform the row operation $R_{1} = R_{1} - R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 0 & - \frac{7}{8} - 0 & 1 - 1 \\ 0 & 0 & 1 \end{array}]$

Schritt 2.4.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{7}{8} & 0 \\ 0 & 0 & 1 \end{array}]$

Schritt 3

Use the result matrix to declare the final solution to the system of equations.

$x - \frac{7}{8} y = 0$

$0 = 1$

Schritt 4

The system is inconsistent so there is no solution.

$Keine Lösung$