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resuelve los siguientes ejercicios segun el enunciado con todo el procedimiento en español 

The exercise asks to perform the matrix multiplication between matrices \( A \) and \( B \):

Given:
\[
A = \begin{pmatrix} 
3 & -5 \\
4 & 1 \\
-2 & -4 
\end{pmatrix}
\quad \text{and} \quad 
B = \begin{pmatrix} 
7 & 4 & -4 & 5 \\
-2 & -3 & 5 & -7 
\end{pmatrix}
\]

We need to compute the product \( A \times B \). 

Let's break it down:

The multiplication of two matrices is done by taking the dot product of the rows of the first matrix with the columns of the second matrix. For matrix \( A \) of size \( 3 \times 2 \) and matrix \( B \) of size \( 2 \times 4 \), the resulting matrix will be of size \( 3 \times 4 \).

Let's calculate the product.The product of matrices \( A \) and \( B \) is:

\[
A \times B = \begin{pmatrix} 
31 & 27 & -37 & 50 \\
26 & 13 & -11 & 13 \\
-6 & 4 & -12 & 18 
\end{pmatrix}
\]

If you have any questions or need more details on the steps, feel free to ask!

Here are some related questions you might consider:
1. How do you perform the dot product for matrix multiplication?
2. What are the conditions for matrix multiplication to be defined?
3. How do you determine the size of the resulting matrix in a multiplication?
4. What happens when you multiply a matrix by an identity matrix?
5. How does matrix multiplication differ from element-wise matrix operations?

**Tip:** Always verify that the number of columns in the first matrix matches the number of rows in the second matrix when performing matrix multiplication.

Realizar el siguiente producto de matrices: A = [[3, -5], [4, 1], [-2, -4]], B = [[7, 4, -4, 5], [-2, -3, 5, -7]]

Learn how to multiply matrices A and B, where A is a 3x2 matrix and B is a 2x4 matrix. This step-by-step solution demonstrates the dot product rule for matrix multiplication. Suitable for students in Grades 10-12.

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