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The problem you're dealing with asks for finding an **elementary matrix** \( E \) such that \( B = EA \), where matrix \( A \) and matrix \( B \) are given. Here's the breakdown of the matrices:

\[
A = \begin{pmatrix} 
8 & 4 & 4 \\
0 & 2 & 8 
\end{pmatrix}
\quad \text{and} \quad 
B = \begin{pmatrix}
8 & 4 & 4 \\
0 & 0 & 8
\end{pmatrix}
\]

Elementary matrices represent row operations, and they are typically formed by applying a specific row operation to the identity matrix. We need to figure out what row operation transforms \( A \) into \( B \).

### Observing the change from \( A \) to \( B \):
- Row 1 stays the same: \( R_1 \) of \( A \) is identical to \( R_1 \) of \( B \).
- Row 2 of \( A \), which is \( (0, 2, 8) \), changes in matrix \( B \) to \( (0, 0, 8) \). This can be achieved by **scaling the second row** by a factor of \( \frac{1}{2} \).

Thus, the elementary matrix \( E \) that represents this row operation is:

\[
E = \begin{pmatrix} 
1 & 0 \\
0 & \frac{1}{2} 
\end{pmatrix}
\]

### Verification:
Now, let's verify if \( B = EA \):

\[
E \cdot A = \begin{pmatrix} 
1 & 0 \\
0 & \frac{1}{2} 
\end{pmatrix} 
\cdot \begin{pmatrix} 
8 & 4 & 4 \\
0 & 2 & 8 
\end{pmatrix}
=
\begin{pmatrix} 
8 & 4 & 4 \\
0 & 1 & 4 
\end{pmatrix}
\]

This matches matrix \( B \), confirming that the elementary matrix is correct.

---

Would you like more details on the steps or any further clarification?

### Follow-up Questions:
1. What are elementary matrices, and how are they related to row operations?
2. How do you verify that a matrix is the result of an elementary row operation?
3. What properties of elementary matrices allow them to represent row operations?
4. Could there be different elementary matrices that achieve the same result for different operations?
5. How are inverse matrices related to elementary row operations?

#### Tip:
Whenever you perform elementary row operations, consider their effect on the identity matrix to generate the corresponding elementary matrix.

Find an elementary matrix E so that B = EA where A = [[8, 4, 4], [0, 2, 8]] and B = [[8, 4, 4], [0, 0, 8]].

In this problem, you are asked to find the elementary matrix E that transforms matrix A into matrix B. The solution involves understanding row operations and applying the concept of elementary matrices.

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