Questions: El resultado de la multiplicación de las siguientes matrices es: 3 -6 1 0 -6 4 0 1 Seleccione una: a. 3-1 -6 4 b. 0 3 c. 3 1 d. 30 0 4

Solution Steps

To solve the problem of finding the result of the multiplication of the given matrices, we need to perform matrix multiplication. The first matrix is a 2x4 matrix, and the second matrix is a 4x1 matrix. The result will be a 2x1 matrix. We will multiply each element of the rows of the first matrix by the corresponding elements of the columns of the second matrix and sum the products.

Definimos las matrices involucradas en la multiplicación: \[ \text{matrix\_a} = \begin{bmatrix} 3 & -6 & 1 & 0 \\ -6 & 4 & 0 & 1 \end{bmatrix} \] \[ \text{matrix\_b} = \begin{bmatrix} 3 \\ -1 \\ 0 \\ 4 \end{bmatrix} \]

Realizamos la multiplicación de las matrices \( \text{matrix\_a} \) y \( \text{matrix\_b} \): \[ \text{result} = \text{matrix\_a} \cdot \text{matrix\_b} \]

Calculamos cada elemento de la matriz resultante:

• Para la primera fila: \[ 15 = 3 \cdot 3 + (-6) \cdot (-1) + 1 \cdot 0 + 0 \cdot 4 = 9 + 6 + 0 + 0 = 15 \]
• Para la segunda fila: \[ -18 = (-6) \cdot 3 + 4 \cdot (-1) + 0 \cdot 0 + 1 \cdot 4 = -18 + 0 + 0 + 4 = -18 \]

Por lo tanto, la matriz resultante es: \[ \text{result} = \begin{bmatrix} 15 \\ -18 \end{bmatrix} \]

Final Answer