Matemática discreta Exemplos

$x \cdot 1 + 4 x \cdot 2 = 14$ , $- 2 x \cdot 1 + 5 x \cdot 2 = 11$

Etapa 1

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

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Etapa 1.1

Simplifique cada termo.

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Etapa 1.1.1

Multiplique $x$ por $1$ .

$x + 4 x \cdot 2 = 14$

$- 2 x \cdot 1 + 5 x \cdot 2 = 11$

Etapa 1.1.2

Multiplique $2$ por $4$ .

$x + 8 x = 14$

$- 2 x \cdot 1 + 5 x \cdot 2 = 11$

$x + 8 x = 14$

$- 2 x \cdot 1 + 5 x \cdot 2 = 11$

Etapa 1.2

Some $x$ e $8 x$ .

$9 x = 14$

$- 2 x \cdot 1 + 5 x \cdot 2 = 11$

Etapa 1.3

Simplifique cada termo.

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Etapa 1.3.1

Multiplique $- 2$ por $1$ .

$9 x = 14$

$- 2 x + 5 x \cdot 2 = 11$

Etapa 1.3.2

Multiplique $2$ por $5$ .

$9 x = 14$

$- 2 x + 10 x = 11$

$9 x = 14$

$- 2 x + 10 x = 11$

Etapa 1.4

Some $- 2 x$ e $10 x$ .

$9 x = 14$

$8 x = 11$

$9 x = 14$

$8 x = 11$

Etapa 2

Write the system as a matrix.

$[\begin{array}{c} 9 & 14 \\ 8 & 11 \end{array}]$

Etapa 3

Encontre a forma escalonada reduzida por linhas.

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Etapa 3.1

Multiply each element of $R_{1}$ by $\frac{1}{9}$ to make the entry at $1, 1$ a $1$ .

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Etapa 3.1.1

Multiply each element of $R_{1}$ by $\frac{1}{9}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{9}{9} & \frac{14}{9} \\ 8 & 11 \end{array}]$

Etapa 3.1.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & \frac{14}{9} \\ 8 & 11 \end{array}]$

Etapa 3.2

Perform the row operation $R_{2} = R_{2} - 8 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Etapa 3.2.1

Perform the row operation $R_{2} = R_{2} - 8 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{14}{9} \\ 8 - 8 \cdot 1 & 11 - 8 (\frac{14}{9}) \end{array}]$

Etapa 3.2.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & \frac{14}{9} \\ 0 & - \frac{13}{9} \end{array}]$

Etapa 3.3

Multiply each element of $R_{2}$ by $- \frac{9}{13}$ to make the entry at $2, 2$ a $1$ .

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Etapa 3.3.1

Multiply each element of $R_{2}$ by $- \frac{9}{13}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{14}{9} \\ - \frac{9}{13} \cdot 0 & - \frac{9}{13} (- \frac{13}{9}) \end{array}]$

Etapa 3.3.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & \frac{14}{9} \\ 0 & 1 \end{array}]$

Etapa 3.4

Perform the row operation $R_{1} = R_{1} - \frac{14}{9} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Etapa 3.4.1

Perform the row operation $R_{1} = R_{1} - \frac{14}{9} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{14}{9} \cdot 0 & \frac{14}{9} - \frac{14}{9} \cdot 1 \\ 0 & 1 \end{array}]$

Etapa 3.4.2

Simplifique $R_{1}$ .

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

Etapa 4

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

$x = 0$

$0 = 1$

Etapa 5

The system is inconsistent so there is no solution.

$Nenhuma solução$