Matemática discreta Exemplos

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} 2 & 1 \\ 4 & 8 \end{array}] - [\begin{array}{c} 3 & 5 \\ 1 & 0 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} 2 & 1 \\ 4 & 8 \end{array}] - [\begin{array}{c} 3 & 5 \\ 1 & 0 \end{array}]$

Etapa 1

Subtraia os elementos correspondentes.

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} 2 - 3 & 1 - 5 \\ 4 - 1 & 8 - 0 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} 2 - 3 & 1 - 5 \\ 4 - 1 & 8 - 0 \end{array}]$

Etapa 2

Simplify each element.

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Etapa 2.1

Subtraia

3

$3$ de

2

$2$ .

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & 1 - 5 \\ 4 - 1 & 8 - 0 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & 1 - 5 \\ 4 - 1 & 8 - 0 \end{array}]$

Etapa 2.2

Subtraia

5

$5$ de

1

$1$ .

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 4 - 1 & 8 - 0 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 4 - 1 & 8 - 0 \end{array}]$

Etapa 2.3

Subtraia

1

$1$ de

4

$4$ .

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 - 0 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 - 0 \end{array}]$

Etapa 2.4

Subtraia

0

$0$ de

8

$8$ .

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}]$

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}]$

Etapa 3

Move all terms not containing a variable to the right side.

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Etapa 3.1

Subtraia

[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]$ dos dois lados da equação.

- x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}] - [\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]

$- x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}] - [\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]$

- x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}] - [\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]

$- x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}] - [\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]$

Etapa 4

Simplifique o lado direito.

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Etapa 4.1

Subtraia os elementos correspondentes.

- x = [\begin{array}{c} - 1 - 1 & - 4 - 10 \\ 3 - 7 & 8 - 6 \end{array}]

$- x = [\begin{array}{c} - 1 - 1 & - 4 - 10 \\ 3 - 7 & 8 - 6 \end{array}]$

Etapa 4.2

Simplify each element.

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Etapa 4.2.1

Subtraia

1

$1$ de

- 1

$- 1$ .

- x = [\begin{array}{c} - 2 & - 4 - 10 \\ 3 - 7 & 8 - 6 \end{array}]

$- x = [\begin{array}{c} - 2 & - 4 - 10 \\ 3 - 7 & 8 - 6 \end{array}]$

Etapa 4.2.2

Subtraia

10

$10$ de

- 4

$- 4$ .

- x = [\begin{array}{c} - 2 & - 14 \\ 3 - 7 & 8 - 6 \end{array}]

$- x = [\begin{array}{c} - 2 & - 14 \\ 3 - 7 & 8 - 6 \end{array}]$

Etapa 4.2.3

Subtraia

7

$7$ de

3

$3$ .

- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 8 - 6 \end{array}]

$- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 8 - 6 \end{array}]$

Etapa 4.2.4

Subtraia

6

$6$ de

8

$8$ .

- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Etapa 5

Multiplique os dois lados por

- 1

$- 1$ .

- - x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$- - x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Etapa 6

Simplifique.

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Etapa 6.1

Multiplique

- - x

$- - x$ .

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Etapa 6.1.1

Multiplique

- 1

$- 1$ por

- 1

$- 1$ .

1 x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$1 x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Etapa 6.1.2

Multiplique

x

$x$ por

1

$1$ .

x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]

$x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Etapa 6.2

Multiplique

- 1

$- 1$ por cada elemento da matriz.

x = [\begin{array}{c} - - 2 & - - 14 \\ - - 4 & - 1 \cdot 2 \end{array}]

$x = [\begin{array}{c} - - 2 & - - 14 \\ - - 4 & - 1 \cdot 2 \end{array}]$

Etapa 6.3

Simplifique cada elemento da matriz.

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Etapa 6.3.1

Multiplique

- 1

$- 1$ por

- 2

$- 2$ .

x = [\begin{array}{c} 2 & - - 14 \\ - - 4 & - 1 \cdot 2 \end{array}]

$x = [\begin{array}{c} 2 & - - 14 \\ - - 4 & - 1 \cdot 2 \end{array}]$

Etapa 6.3.2

Multiplique

- 1

$- 1$ por

- 14

$- 14$ .

x = [\begin{array}{c} 2 & 14 \\ - - 4 & - 1 \cdot 2 \end{array}]

$x = [\begin{array}{c} 2 & 14 \\ - - 4 & - 1 \cdot 2 \end{array}]$

Etapa 6.3.3

Multiplique

- 1

$- 1$ por

- 4

$- 4$ .

x = [\begin{array}{c} 2 & 14 \\ 4 & - 1 \cdot 2 \end{array}]

$x = [\begin{array}{c} 2 & 14 \\ 4 & - 1 \cdot 2 \end{array}]$

Etapa 6.3.4

Multiplique

- 1

$- 1$ por

2

$2$ .

x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]

$x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]$

x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]

$x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]$

x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]

$x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]$