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The transpose of the matrix \( E \) is:

\[
E^T = \begin{pmatrix}
-2 & 3 \\
\frac{1}{7} & 6 \\
-5 & -3 \\
0 & 1
\end{pmatrix}
\]

In decimal form, it can be written as:

\[
E^T \approx \begin{pmatrix}
-2 & 3 \\
0.1429 & 6 \\
-5 & -3 \\
0 & 1
\end{pmatrix}
\]

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### Related Questions:
1. What is the significance of matrix transposition in linear algebra?
2. How do you calculate the determinant of a square matrix?
3. What are the properties of transpose matrices?
4. Can you explain how matrix multiplication works with transpose matrices?
5. How does the transpose operation affect the eigenvalues and eigenvectors of a matrix?

**Tip:** Remember that the transpose of a matrix flips it over its diagonal, converting rows to columns and vice versa.

Explore the transpose of matrix E with detailed steps and decimal approximation. Understand matrix operations and linear algebra concepts. Suitable for advanced high school students and anyone interested in matrix mathematics.

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