Álgebra lineal Ejemplos

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

Paso 1

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

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

Paso 2

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 2.1

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

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

Paso 2.2

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 2.3

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 2.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 2.5

Suma $1$ y $1$ .

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

Paso 2.6

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

Toca para ver más pasos...

Paso 2.6.1

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

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

Paso 2.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 2.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 2.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 2.6.4.1

Cancela el factor común.

Paso 2.6.4.2

Reescribe la expresión.

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

Paso 2.6.5

Evalúa el exponente.

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

Paso 3

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

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

Paso 4

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 4.1

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

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

Paso 4.2

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 4.3

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 4.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 4.5

Suma $1$ y $1$ .

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

Paso 4.6

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

Toca para ver más pasos...

Paso 4.6.1

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

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

Paso 4.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 4.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 4.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 4.6.4.1

Cancela el factor común.

Paso 4.6.4.2

Reescribe la expresión.

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

Paso 4.6.5

Evalúa el exponente.

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

Paso 5

Cancela el factor común de $2$ y $22$ .

Toca para ver más pasos...

Paso 5.1

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

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

Paso 5.2

Cancela los factores comunes.

Toca para ver más pasos...

Paso 5.2.1

Factoriza $2$ de $22$ .

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

Paso 5.2.2

Cancela el factor común.

Paso 5.2.3

Reescribe la expresión.

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

Paso 6

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

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

Paso 7

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 7.1

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

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

Paso 7.2

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 7.3

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 7.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 7.5

Suma $1$ y $1$ .

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

Paso 7.6

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

Toca para ver más pasos...

Paso 7.6.1

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

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

Paso 7.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 7.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 7.6.4

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 7.6.4.1

Cancela el factor común.

Paso 7.6.4.2

Reescribe la expresión.

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

Paso 7.6.5

Evalúa el exponente.

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

Paso 8

Cancela el factor común de $4$ y $22$ .

Toca para ver más pasos...

Paso 8.1

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

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

Paso 8.2

Cancela los factores comunes.

Toca para ver más pasos...

Paso 8.2.1

Factoriza $2$ de $22$ .

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

Paso 8.2.2

Cancela el factor común.

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

Paso 8.2.3

Reescribe la expresión.

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

Paso 9

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

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

Paso 10

Combina y simplifica el denominador.

Toca para ver más pasos...

Paso 10.1

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

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

Paso 10.2

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 10.3

Eleva $\sqrt{22}$ a la potencia de $1$ .

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

Paso 10.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Paso 10.5

Suma $1$ y $1$ .

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

Paso 10.6

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

Toca para ver más pasos...

Paso 10.6.1

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

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

Paso 10.6.2

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 10.6.3

Combina $\frac{1}{2}$ y $2$ .

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

Paso 10.6.4

Cancela el factor común de $2$ .

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Paso 10.6.4.1

Cancela el factor común.

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

Paso 10.6.4.2

Reescribe la expresión.

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

Paso 10.6.5

Evalúa el exponente.

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

Paso 11

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

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Paso 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 $4 \times 2$ .

Paso 11.2

Multiplica cada fila en la primera matriz por cada columna en la segunda matriz.

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

Paso 11.3

Simplifica cada elemento de la matriz mediante la multiplicación de todas las expresiones.

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