Álgebra linear Exemplos

2 [\begin{array}{c} 1 & 8 \\ 2 & 1 \end{array}] + 4

$2 [\begin{array}{c} 1 & 8 \\ 2 & 1 \end{array}] + 4$

Etapa 1

Simplifique cada termo.

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Etapa 1.1

Multiplique

2

$2$ por cada elemento da matriz.

[\begin{array}{c} 2 \cdot 1 & 2 \cdot 8 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4

$[\begin{array}{c} 2 \cdot 1 & 2 \cdot 8 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4$

Etapa 1.2

Simplifique cada elemento da matriz.

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Etapa 1.2.1

Multiplique

2

$2$ por

1

$1$ .

[\begin{array}{c} 2 & 2 \cdot 8 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4

$[\begin{array}{c} 2 & 2 \cdot 8 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4$

Etapa 1.2.2

Multiplique

2

$2$ por

8

$8$ .

[\begin{array}{c} 2 & 16 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4

$[\begin{array}{c} 2 & 16 \\ 2 \cdot 2 & 2 \cdot 1 \end{array}] + 4$

Etapa 1.2.3

Multiplique

2

$2$ por

2

$2$ .

[\begin{array}{c} 2 & 16 \\ 4 & 2 \cdot 1 \end{array}] + 4

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \cdot 1 \end{array}] + 4$

Etapa 1.2.4

Multiplique

2

$2$ por

1

$1$ .

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4$

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4$

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4$

Etapa 2

Adding

4

$4$ to a

2 \times 2

$2 \times 2$ square matrix is the same as adding

4

$4$ times the

2 \times 2

$2 \times 2$ identity matrix.

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4 [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + 4 [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Etapa 3

Multiplique

4

$4$ por cada elemento da matriz.

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 \cdot 1 & 4 \cdot 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 \cdot 1 & 4 \cdot 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]$

Etapa 4

Simplifique cada elemento da matriz.

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Etapa 4.1

Multiplique

4

$4$ por

1

$1$ .

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 4 \cdot 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 4 \cdot 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]$

Etapa 4.2

Multiplique

4

$4$ por

0

$0$ .

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 4 \cdot 0 & 4 \cdot 1 \end{array}]$

Etapa 4.3

Multiplique

4

$4$ por

0

$0$ .

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \cdot 1 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \cdot 1 \end{array}]$

Etapa 4.4

Multiplique

4

$4$ por

1

$1$ .

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \end{array}]$

[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \end{array}]

$[\begin{array}{c} 2 & 16 \\ 4 & 2 \end{array}] + [\begin{array}{c} 4 & 0 \\ 0 & 4 \end{array}]$

Etapa 5

Adicione os elementos correspondentes.

[\begin{array}{c} 2 + 4 & 16 + 0 \\ 4 + 0 & 2 + 4 \end{array}]

$[\begin{array}{c} 2 + 4 & 16 + 0 \\ 4 + 0 & 2 + 4 \end{array}]$

Etapa 6

Simplify each element.

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Etapa 6.1

Some

2

$2$ e

4

$4$ .

[\begin{array}{c} 6 & 16 + 0 \\ 4 + 0 & 2 + 4 \end{array}]

$[\begin{array}{c} 6 & 16 + 0 \\ 4 + 0 & 2 + 4 \end{array}]$

Etapa 6.2

Some

16

$16$ e

0

$0$ .

[\begin{array}{c} 6 & 16 \\ 4 + 0 & 2 + 4 \end{array}]

$[\begin{array}{c} 6 & 16 \\ 4 + 0 & 2 + 4 \end{array}]$

Etapa 6.3

Some

4

$4$ e

0

$0$ .

[\begin{array}{c} 6 & 16 \\ 4 & 2 + 4 \end{array}]

$[\begin{array}{c} 6 & 16 \\ 4 & 2 + 4 \end{array}]$

Etapa 6.4

Some

2

$2$ e

4

$4$ .

[\begin{array}{c} 6 & 16 \\ 4 & 6 \end{array}]

$[\begin{array}{c} 6 & 16 \\ 4 & 6 \end{array}]$

[\begin{array}{c} 6 & 16 \\ 4 & 6 \end{array}]

$[\begin{array}{c} 6 & 16 \\ 4 & 6 \end{array}]$