Finite Mathematik Beispiele

$- 4 x + 4 y = 4$ , $3 x - 3 y = - 3$

Schritt 1

Write the system as a matrix.

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

Schritt 2

Ermittele die normierte Zeilenstufenform.

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Schritt 2.1

Multiply each element of $R_{1}$ by $- \frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

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Schritt 2.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot 4 & - \frac{1}{4} \cdot 4 \\ 3 & - 3 & - 3 \end{array}]$

Schritt 2.1.2

Vereinfache $R_{1}$ .

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

Schritt 2.2

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

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Schritt 2.2.1

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

$[\begin{array}{c} 1 & - 1 & - 1 \\ 3 - 3 \cdot 1 & - 3 - 3 \cdot - 1 & - 3 - 3 \cdot - 1 \end{array}]$

Schritt 2.2.2

Vereinfache $R_{2}$ .

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

Schritt 3

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

$x - y = - 1$

$0 = 0$

Schritt 4

The solution is the set of ordered pairs that make the system true.

$(- 1 + y, y)$