Matematica discreta Esempi

$x + 6 y - 3 z = - 5$ , $z = 8$

Passaggio 1

Write the system as a matrix.

$[\begin{array}{c} 1 & 6 & - 3 & - 5 \\ 0 & 0 & 1 & 8 \end{array}]$

Passaggio 2

Trova la forma ridotta a scala per righe di Echelon.

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Passaggio 2.1

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

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Passaggio 2.1.1

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

$[\begin{array}{c} 1 + 3 \cdot 0 & 6 + 3 \cdot 0 & - 3 + 3 \cdot 1 & - 5 + 3 \cdot 8 \\ 0 & 0 & 1 & 8 \end{array}]$

Passaggio 2.1.2

Semplifica $R_{1}$ .

$[\begin{array}{c} 1 & 6 & 0 & 19 \\ 0 & 0 & 1 & 8 \end{array}]$

Passaggio 3

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

$x + 6 y = 19$

$z = 8$

Passaggio 4

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

$(19 - 6 y, y, 8)$