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: \[ \boxed{5} \]

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El valor de \( m \) es 5.
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