Álgebra Exemplos

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + 34$

Etapa 1

Adding $34$ to a $4 \times 4$ square matrix is the same as adding $34$ times the $4 \times 4$ identity matrix.

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + 34 [\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

Etapa 2

Multiplique $34$ por cada elemento da matriz.

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3

Simplifique cada elemento da matriz.

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Etapa 3.1

Multiplique $34$ por $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.2

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.3

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.4

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.5

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 \cdot 1 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.6

Multiplique $34$ por $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 34 \cdot 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.7

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.8

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.9

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 34 \cdot 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.10

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 \cdot 1 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.11

Multiplique $34$ por $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 34 \cdot 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.12

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.13

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 34 \cdot 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.14

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 0 & 34 \cdot 0 & 34 \cdot 1 \end{array}]$

Etapa 3.15

Multiplique $34$ por $0$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 0 & 0 & 34 \cdot 1 \end{array}]$

Etapa 3.16

Multiplique $34$ por $1$ .

$[\begin{array}{c} 2 & 4 & 6 & 8 \\ 10 & 12 & 14 & 16 \\ 18 & 20 & 22 & 24 \\ 26 & 28 & 30 & 32 \end{array}] + [\begin{array}{c} 34 & 0 & 0 & 0 \\ 0 & 34 & 0 & 0 \\ 0 & 0 & 34 & 0 \\ 0 & 0 & 0 & 34 \end{array}]$

Etapa 4

Adicione os elementos correspondentes.

$[\begin{array}{c} 2 + 34 & 4 + 0 & 6 + 0 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5

Simplify each element.

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Etapa 5.1

Some $2$ e $34$ .

$[\begin{array}{c} 36 & 4 + 0 & 6 + 0 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.2

Some $4$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 + 0 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.3

Some $6$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 + 0 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.4

Some $8$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 + 0 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.5

Some $10$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 12 + 34 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.6

Some $12$ e $34$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 + 0 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.7

Some $14$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 + 0 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.8

Some $16$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 + 0 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.9

Some $18$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 + 0 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.10

Some $20$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 22 + 34 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.11

Some $22$ e $34$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 + 0 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.12

Some $24$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 + 0 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.13

Some $26$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 + 0 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.14

Some $28$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 & 30 + 0 & 32 + 34 \end{array}]$

Etapa 5.15

Some $30$ e $0$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 & 30 & 32 + 34 \end{array}]$

Etapa 5.16

Some $32$ e $34$ .

$[\begin{array}{c} 36 & 4 & 6 & 8 \\ 10 & 46 & 14 & 16 \\ 18 & 20 & 56 & 24 \\ 26 & 28 & 30 & 66 \end{array}]$