Warren Watson
11/23/2023 · Middle School
Halla el valor de m, para que el determinante de A sea igual a -25 \( A=\left(\begin{array}{cc}m & 5 \\ 2 & -3\end{array}\right) \)
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Para encontrar el valor de \( m \) tal que el determinante de la matriz \( A \) sea igual a -25, primero calculamos el determinante de la matriz \( A \):
\[
A = \begin{pmatrix} m & 5 \\ 2 & -3 \end{pmatrix}
\]
El determinante de una matriz \( 2 \times 2 \) se calcula con la fórmula:
\[
\text{det}(A) = ad - bc
\]
donde \( a, b, c, d \) son los elementos de la matriz:
\[
\text{det}(A) = m \cdot (-3) - 5 \cdot 2
\]
Calculamos esto:
\[
\text{det}(A) = -3m - 10
\]
Queremos que este determinante sea igual a -25:
\[
-3m - 10 = -25
\]
Ahora, resolvemos la ecuación para \( m \):
1. Sumamos 10 a ambos lados:
\[
-3m = -25 + 10
\]
\[
-3m = -15
\]
2. Dividimos ambos lados entre -3:
\[
m = \frac{-15}{-3} = 5
\]
Por lo tanto, el valor de \( m \) que hace que el determinante de \( A \) sea igual a -25 es:
\[
\boxed{5}
\]
Quick Answer
El valor de \( m \) es 5.
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