find row reduced echelon form of A = rows 1.[-2,-9,-33,-22]  2.[1,4,15,10]  3.[1,3,12,8] 4.[-3,-9,-36,-24]

The row reduced echelon form (RREF) of the matrix \( A \) is:

\[
\begin{pmatrix}
1 & 0 & 3 & 2 \\
0 & 1 & 3 & 2 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{pmatrix}
\]

This matrix is in its simplest form where the leading entries in each row are 1, and all the other elements in the pivot columns are 0.

Do you have any questions or would you like more details on the process?

Here are some related questions to explore:
1. What is the significance of the pivot columns in the RREF of a matrix?
2. How do you interpret the zero rows in the row reduced echelon form?
3. What are the applications of row reduced echelon forms in solving linear systems?
4. How can you determine the rank of a matrix from its RREF?
5. How does the RREF help in finding the inverse of a matrix?
6. What is the difference between the row echelon form and row reduced echelon form?
7. Can every matrix be transformed into an RREF?
8. How do elementary row operations affect the determinant of a matrix?

**Tip:** Always check for consistent equations when using RREF to solve linear systems, as it will reveal any dependencies or inconsistencies.

Learn how to find the row reduced echelon form (RREF) of a matrix A = [[-2, -9, -33, -22], [1, 4, 15, 10], [1, 3, 12, 8], [-3, -9, -36, -24]]. This solution provides a step-by-step process to transform the matrix into its simplest form where the leading entries in each row are 1, and all other elements in the pivot columns are 0. Suitable for advanced high school students studying linear algebra.

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