https://file.aiquickdraw.com/mathbot/file/1726762815488ie55mlon.jpg

The matrix in the image is written in its regular form, but I assume you are asking for its normal form, possibly the reduced row echelon form (RREF).

The given matrix is:

\[
\begin{bmatrix}
1 & 2 & -1 & 4 \\
2 & 4 & 3 & 4 \\
1 & 2 & 3 & 4 \\
-1 & -2 & 6 & -7
\end{bmatrix}
\]

I will compute the reduced row echelon form for you.The matrix in its reduced row echelon form (RREF) is:

\[
\begin{bmatrix}
1 & 2 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0
\end{bmatrix}
\]

This is the normal form of the matrix.

Would you like a detailed explanation of how this transformation was done or have any other questions?

Here are 5 related questions to consider:
1. What is the significance of a matrix being in reduced row echelon form?
2. How can the RREF be used to solve systems of linear equations?
3. What is the difference between echelon form and reduced row echelon form?
4. How do pivot columns determine the rank of a matrix?
5. How can the determinant be calculated for square matrices?

**Tip:** To efficiently row-reduce a matrix, focus on creating leading 1s in each row while systematically eliminating the other entries in the same column.

Learn how to convert a matrix into its normal form using row operations. This example demonstrates how to find the reduced row echelon form (RREF) of a 4x4 matrix, with key concepts in linear algebra. Suitable for undergraduate students.

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