Bowman Smith
09/11/2024 · High School
Semana 2 Dadas las matrices \( \mathrm{A}=\left(\begin{array}{ll}3 & 7 \\ 5 & 9 \\ 7 & 1\end{array}\right) \quad \mathrm{B}=\left(\begin{array}{ll}-1 & 2 \\ -2 & 2 \\ -3 & 4\end{array}\right) \)
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Para trabajar con las matrices \( \mathrm{A} \) y \( \mathrm{B} \), primero observemos sus dimensiones:
- La matriz \( \mathrm{A} \) es de tamaño \( 3 \times 2 \) (3 filas y 2 columnas).
- La matriz \( \mathrm{B} \) también es de tamaño \( 3 \times 2 \).
Dado que ambas matrices tienen el mismo número de filas y columnas, podemos realizar operaciones como la suma o la resta de matrices.
### Suma de matrices
La suma de las matrices \( \mathrm{A} \) y \( \mathrm{B} \) se realiza sumando los elementos correspondientes:
\[
\mathrm{C} = \mathrm{A} + \mathrm{B} = \left(\begin{array}{cc}3 & 7 \\ 5 & 9 \\ 7 & 1\end{array}\right) + \left(\begin{array}{cc}-1 & 2 \\ -2 & 2 \\ -3 & 4\end{array}\right) = \left(\begin{array}{cc}3 + (-1) & 7 + 2 \\ 5 + (-2) & 9 + 2 \\ 7 + (-3) & 1 + 4\end{array}\right)
\]
Calculando cada elemento:
\[
\mathrm{C} = \left(\begin{array}{cc}2 & 9 \\ 3 & 11 \\ 4 & 5\end{array}\right)
\]
### Resta de matrices
La resta de las matrices \( \mathrm{A} \) y \( \mathrm{B} \) se realiza restando los elementos correspondientes:
\[
\mathrm{D} = \mathrm{A} - \mathrm{B} = \left(\begin{array}{cc}3 & 7 \\ 5 & 9 \\ 7 & 1\end{array}\right) - \left(\begin{array}{cc}-1 & 2 \\ -2 & 2 \\ -3 & 4\end{array}\right) = \left(\begin{array}{cc}3 - (-1) & 7 - 2 \\ 5 - (-2) & 9 - 2 \\ 7 - (-3) & 1 - 4\end{array}\right)
\]
Calculando cada elemento:
\[
\mathrm{D} = \left(\begin{array}{cc}4 & 5 \\ 7 & 7 \\ 10 & -3\end{array}\right)
\]
### Resumen
- La suma de las matrices \( \mathrm{A} \) y \( \mathrm{B} \) es:
\[
\mathrm{C} = \left(\begin{array}{cc}2 & 9 \\ 3 & 11 \\ 4 & 5\end{array}\right)
\]
- La resta de las matrices \( \mathrm{A} \) y \( \mathrm{B} \) es:
\[
\mathrm{D} = \left(\begin{array}{cc}4 & 5 \\ 7 & 7 \\ 10 & -3\end{array}\right)
\]
Quick Answer
La suma de las matrices \( \mathrm{A} \) y \( \mathrm{B} \) es \( \mathrm{C} = \left(\begin{array}{cc}2 & 9 \\ 3 & 11 \\ 4 & 5\end{array}\right) \) y la resta es \( \mathrm{D} = \left(\begin{array}{cc}4 & 5 \\ 7 & 7 \\ 10 & -3\end{array}\right) \).
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