https://file.aiquickdraw.com/mathbot/file/1731071160381j9xao9o0.jpg

Let's work through this matrix multiplication problem step by step.

### Problem Statement
We are given two matrices:
\[
A = \begin{bmatrix} 3 & 0 & 1 \\ 5 & 5 & 6 \end{bmatrix}
\]
\[
B = \begin{bmatrix} 4 & 7 \\ 7 & 7 \end{bmatrix}
\]

We need to calculate \( A \times B \).

### Step 1: Confirm Matrix Dimensions
Matrix \( A \) has dimensions \( 2 \times 3 \) (2 rows, 3 columns), and matrix \( B \) has dimensions \( 2 \times 2 \) (2 rows, 2 columns).

For matrix multiplication to be possible, the number of columns in \( A \) must equal the number of rows in \( B \). Since \( A \) has 3 columns and \( B \) has 2 rows, **the multiplication \( A \times B \) is not defined** because the inner dimensions do not match.

### Conclusion
Matrix multiplication \( A \times B \) is undefined in this case because the dimensions do not align correctly for multiplication.

Would you like to ask about a related concept, or do you have any questions?

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Here are 5 related questions to deepen understanding:

1. **What are the rules for matrix multiplication regarding dimensions?**
2. **How can we verify if two matrices can be multiplied?**
3. **What does it mean if matrix multiplication is undefined?**
4. **How is matrix multiplication different from element-wise multiplication?**
5. **Can matrix multiplication be commutative?**

**Tip:** Always verify the dimensions of matrices before performing operations like multiplication.

Explore the matrix multiplication problem with matrices A and B, including a step-by-step breakdown. Learn the importance of matrix dimensions in determining if the multiplication is defined. Suitable for high school students in Grades 10-12.

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