Álgebra linear Exemplos

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{1}{\sqrt{22}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 1

Multiplique $\frac{1}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{1}{\sqrt{22}} \cdot \frac{\sqrt{22}}{\sqrt{22}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2

Combine e simplifique o denominador.

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Etapa 2.1

Multiplique $\frac{1}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{\sqrt{22} \sqrt{22}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.2

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{{\sqrt{22}}^{1} \sqrt{22}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.3

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{{\sqrt{22}}^{1} {\sqrt{22}}^{1}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.4

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{{\sqrt{22}}^{1 + 1}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.5

Some $1$ e $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{{\sqrt{22}}^{2}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.6

Reescreva ${\sqrt{22}}^{2}$ como $22$ .

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Etapa 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{22}$ como $22^{\frac{1}{2}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{{(22^{\frac{1}{2}})}^{2}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.6.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22^{\frac{1}{2} \cdot 2}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.6.3

Combine $\frac{1}{2}$ e $2$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22^{\frac{2}{2}}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.6.4

Cancele o fator comum de $2$ .

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Etapa 2.6.4.1

Cancele o fator comum.

Etapa 2.6.4.2

Reescreva a expressão.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22^{1}} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 2.6.5

Avalie o expoente.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 3

Multiplique $\frac{2}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2}{\sqrt{22}} \cdot \frac{\sqrt{22}}{\sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4

Combine e simplifique o denominador.

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Etapa 4.1

Multiplique $\frac{2}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{\sqrt{22} \sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.2

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{{\sqrt{22}}^{1} \sqrt{22}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.3

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{{\sqrt{22}}^{1} {\sqrt{22}}^{1}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.4

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{{\sqrt{22}}^{1 + 1}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.5

Some $1$ e $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{{\sqrt{22}}^{2}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.6

Reescreva ${\sqrt{22}}^{2}$ como $22$ .

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Etapa 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{22}$ como $22^{\frac{1}{2}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{{(22^{\frac{1}{2}})}^{2}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.6.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{22^{\frac{1}{2} \cdot 2}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.6.3

Combine $\frac{1}{2}$ e $2$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{22^{\frac{2}{2}}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.6.4

Cancele o fator comum de $2$ .

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Etapa 4.6.4.1

Cancele o fator comum.

Etapa 4.6.4.2

Reescreva a expressão.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{22^{1}} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 4.6.5

Avalie o expoente.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{22} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 5

Cancele o fator comum de $2$ e $22$ .

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Etapa 5.1

Fatore $2$ de $2 \sqrt{22}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 (\sqrt{22})}{22} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 5.2

Cancele os fatores comuns.

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Etapa 5.2.1

Fatore $2$ de $22$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{2 \sqrt{22}}{2 \cdot 11} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 5.2.2

Cancele o fator comum.

Etapa 5.2.3

Reescreva a expressão.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4}{\sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 6

Multiplique $\frac{4}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - (\frac{4}{\sqrt{22}} \cdot \frac{\sqrt{22}}{\sqrt{22}}) & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7

Combine e simplifique o denominador.

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Etapa 7.1

Multiplique $\frac{4}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{\sqrt{22} \sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.2

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{{\sqrt{22}}^{1} \sqrt{22}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.3

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{{\sqrt{22}}^{1} {\sqrt{22}}^{1}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.4

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{{\sqrt{22}}^{1 + 1}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.5

Some $1$ e $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{{\sqrt{22}}^{2}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.6

Reescreva ${\sqrt{22}}^{2}$ como $22$ .

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Etapa 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{22}$ como $22^{\frac{1}{2}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{{(22^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.6.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{22^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.6.3

Combine $\frac{1}{2}$ e $2$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{22^{\frac{2}{2}}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.6.4

Cancele o fator comum de $2$ .

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Etapa 7.6.4.1

Cancele o fator comum.

Etapa 7.6.4.2

Reescreva a expressão.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{22^{1}} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 7.6.5

Avalie o expoente.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{4 \sqrt{22}}{22} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 8

Cancele o fator comum de $4$ e $22$ .

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Etapa 8.1

Fatore $2$ de $4 \sqrt{22}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 (2 \sqrt{22})}{22} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 8.2

Cancele os fatores comuns.

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Etapa 8.2.1

Fatore $2$ de $22$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 (2 \sqrt{22})}{2 (11)} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 8.2.2

Cancele o fator comum.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 (2 \sqrt{22})}{2 \cdot 11} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 8.2.3

Reescreva a expressão.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{1}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 9

Multiplique $\frac{1}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{1}{\sqrt{22}} \cdot \frac{\sqrt{22}}{\sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10

Combine e simplifique o denominador.

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Etapa 10.1

Multiplique $\frac{1}{\sqrt{22}}$ por $\frac{\sqrt{22}}{\sqrt{22}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{\sqrt{22} \sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.2

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{{\sqrt{22}}^{1} \sqrt{22}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.3

Eleve $\sqrt{22}$ à potência de $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{{\sqrt{22}}^{1} {\sqrt{22}}^{1}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.4

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{{\sqrt{22}}^{1 + 1}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.5

Some $1$ e $1$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{{\sqrt{22}}^{2}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.6

Reescreva ${\sqrt{22}}^{2}$ como $22$ .

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Etapa 10.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{22}$ como $22^{\frac{1}{2}}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{{(22^{\frac{1}{2}})}^{2}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.6.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{22^{\frac{1}{2} \cdot 2}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.6.3

Combine $\frac{1}{2}$ e $2$ .

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{22^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.6.4

Cancele o fator comum de $2$ .

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Etapa 10.6.4.1

Cancele o fator comum.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{22^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.6.4.2

Reescreva a expressão.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{22^{1}} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 10.6.5

Avalie o expoente.

$[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{22} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$

Etapa 11

Multiplique $[\begin{array}{c} \frac{2}{7} & \frac{5}{7} & \frac{2}{7} & - \frac{4}{7} \\ \frac{\sqrt{22}}{22} & \frac{\sqrt{22}}{11} & - \frac{2 \sqrt{22}}{11} & \frac{\sqrt{22}}{22} \end{array}] [\begin{array}{c} 2 & 3 \\ 5 & 7 \\ 2 & - 2 \\ - 4 & - 3 \end{array}]$ .

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Etapa 11.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $2 \times 4$ and the second matrix is $4 \times 2$ .

Etapa 11.2

Multiplique cada linha na primeira matriz por cada coluna na segunda matriz.

$[\begin{array}{c} \frac{2}{7} \cdot 2 + \frac{5}{7} \cdot 5 + \frac{2}{7} \cdot 2 - \frac{4}{7} \cdot - 4 & \frac{2}{7} \cdot 3 + \frac{5}{7} \cdot 7 + \frac{2}{7} \cdot - 2 - \frac{4}{7} \cdot - 3 \\ \frac{\sqrt{22}}{22} \cdot 2 + \frac{\sqrt{22}}{11} \cdot 5 - \frac{2 \sqrt{22}}{11} \cdot 2 + \frac{\sqrt{22}}{22} \cdot - 4 & \frac{\sqrt{22}}{22} \cdot 3 + \frac{\sqrt{22}}{11} \cdot 7 - \frac{2 \sqrt{22}}{11} \cdot - 2 + \frac{\sqrt{22}}{22} \cdot - 3 \end{array}]$

Etapa 11.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

$[\begin{array}{c} 7 & 7 \\ 0 & \sqrt{22} \end{array}]$