Finite Mathematik Beispiele

$4 x - 5 x = 5$ , $- 8 x + 10 x = 5$

Schritt 1

Move variables to the left and constant terms to the right.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.1

Subtrahiere $5 x$ von $4 x$ .

$- x = 5$

$- 8 x + 10 x = 5$

Schritt 1.2

Addiere $- 8 x$ und $10 x$ .

$- x = 5$

$2 x = 5$

$- x = 5$

$2 x = 5$

Schritt 2

Write the system as a matrix.

$[\begin{array}{c} - 1 & 5 \\ 2 & 5 \end{array}]$

Schritt 3

Ermittele die normierte Zeilenstufenform.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.1

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

Tippen, um mehr Schritte zu sehen ...

Schritt 3.1.1

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

$[\begin{array}{c} - - 1 & - 1 \cdot 5 \\ 2 & 5 \end{array}]$

Schritt 3.1.2

Vereinfache $R_{1}$ .

$[\begin{array}{c} 1 & - 5 \\ 2 & 5 \end{array}]$

Schritt 3.2

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

Tippen, um mehr Schritte zu sehen ...

Schritt 3.2.1

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

$[\begin{array}{c} 1 & - 5 \\ 2 - 2 \cdot 1 & 5 - 2 \cdot - 5 \end{array}]$

Schritt 3.2.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - 5 \\ 0 & 15 \end{array}]$

Schritt 3.3

Multiply each element of $R_{2}$ by $\frac{1}{15}$ to make the entry at $2, 2$ a $1$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 3.3.1

Multiply each element of $R_{2}$ by $\frac{1}{15}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 5 \\ \frac{0}{15} & \frac{15}{15} \end{array}]$

Schritt 3.3.2

Vereinfache $R_{2}$ .

$[\begin{array}{c} 1 & - 5 \\ 0 & 1 \end{array}]$

Schritt 3.4

Perform the row operation $R_{1} = R_{1} + 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 3.4.1

Perform the row operation $R_{1} = R_{1} + 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + 5 \cdot 0 & - 5 + 5 \cdot 1 \\ 0 & 1 \end{array}]$

Schritt 3.4.2

Vereinfache $R_{1}$ .

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

Schritt 4

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

$x = 0$

$0 = 1$

Schritt 5

The system is inconsistent so there is no solution.

$Keine Lösung$