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To solve the problem of finding the order of the resulting matrix after multiplying two matrices, we need to examine the dimensions (or order) of the given matrices.

The first matrix on the left side is a 5x5 matrix (5 rows and 5 columns), and the second matrix on the right side is a 5x1 matrix (5 rows and 1 column).

### Matrix Multiplication Rule:
When multiplying two matrices, \( A \) (of order \( m \times n \)) and \( B \) (of order \( n \times p \)), the resulting matrix will have the order \( m \times p \).

### Applying the Rule:
- The first matrix is of order \( 5 \times 5 \) (5 rows and 5 columns).
- The second matrix is of order \( 5 \times 1 \) (5 rows and 1 column).

The number of columns in the first matrix (5) is equal to the number of rows in the second matrix (5), so matrix multiplication is possible.

The resulting matrix will have the number of rows of the first matrix and the number of columns of the second matrix:

\[
\text{Resulting Matrix Order} = 5 \times 1
\]

### Conclusion:
The order of the resulting matrix after multiplying the given matrices is **5x1**.

Would you like more details or have any questions?

### Related Questions:
1. What is the definition of matrix multiplication?
2. How do you compute the elements of the resulting matrix in matrix multiplication?
3. What are the properties of matrix multiplication?
4. Can you multiply matrices of any size? Why or why not?
5. How can matrix multiplication be applied in real-world scenarios?

#### Tip:
Matrix multiplication is not commutative; that is, in general, \( AB \neq BA \).

What will be the ORDER of the resulting matrix after multiplying the two matrices below?

Determine the order of the resulting matrix after multiplying a 5x5 matrix and a 5x1 matrix. This matrix multiplication problem focuses on linear algebra and matrix dimensions. Suitable for Grades 9-12.

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