Matemática discreta Exemplos

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 1

Multiplique os dois lados por $1$ .

$1 ([\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}]) = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2

Simplifique.

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Etapa 2.1

Multiplique $1$ por cada elemento da matriz.

$[\begin{array}{c} 1 (a + 10) & 1 (9 z + 1) & 1 (2 m) \\ 1 (6 k) & 1 \cdot 2 & 1 \cdot 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.2

Simplifique cada elemento da matriz.

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Etapa 2.2.1

Multiplique $a + 10$ por $1$ .

$[\begin{array}{c} a + 10 & 1 (9 z + 1) & 1 (2 m) \\ 1 (6 k) & 1 \cdot 2 & 1 \cdot 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.2.2

Multiplique $9 z + 1$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 1 (2 m) \\ 1 (6 k) & 1 \cdot 2 & 1 \cdot 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.2.3

Multiplique $2 m$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 1 (6 k) & 1 \cdot 2 & 1 \cdot 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.2.4

Multiplique $6 k$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 1 \cdot 2 & 1 \cdot 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.2.5

Multiplique $2$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \cdot 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.2.6

Multiplique $1$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = 1 [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$

Etapa 2.3

Multiplique $1$ por cada elemento da matriz.

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 1 \cdot 20 & 1 \cdot - 32 & 1 \cdot 90 \\ 1 \cdot 45 & 1 \cdot 4 & 1 \cdot 4 \end{array}]$

Etapa 2.4

Simplifique cada elemento da matriz.

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Etapa 2.4.1

Multiplique $20$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & 1 \cdot - 32 & 1 \cdot 90 \\ 1 \cdot 45 & 1 \cdot 4 & 1 \cdot 4 \end{array}]$

Etapa 2.4.2

Multiplique $- 32$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & - 32 & 1 \cdot 90 \\ 1 \cdot 45 & 1 \cdot 4 & 1 \cdot 4 \end{array}]$

Etapa 2.4.3

Multiplique $90$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & - 32 & 90 \\ 1 \cdot 45 & 1 \cdot 4 & 1 \cdot 4 \end{array}]$

Etapa 2.4.4

Multiplique $45$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 1 \cdot 4 & 1 \cdot 4 \end{array}]$

Etapa 2.4.5

Multiplique $4$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 1 \cdot 4 \end{array}]$

Etapa 2.4.6

Multiplique $4$ por $1$ .

$[\begin{array}{c} a + 10 & 9 z + 1 & 2 m \\ 6 k & 2 & 1 \end{array}] [\begin{array}{c} 9 a & 2 z & 8 m \\ 9 k & 2 & 3 \end{array}] = [\begin{array}{c} 20 & - 32 & 90 \\ 45 & 4 & 4 \end{array}]$