https://file.aiquickdraw.com/mathbot/file/172633063005389umi5z6.jpg

The matrix given in the image is:

\[
\begin{pmatrix}
1 & 1 & 0 & -5 \\
0 & 0 & 1 & 3
\end{pmatrix}
\]

To check if a matrix is in row-reduced echelon form (RREF), the following conditions must be satisfied:
1. **Leading 1s:** Each leading entry in a row must be 1.
2. **Zeroes in the column of leading 1s:** The leading 1 must be the only non-zero entry in its column.
3. **Rows of zeroes:** Any rows that consist entirely of zeroes are at the bottom.
4. **Staircase form:** The leading 1 in each row must appear to the right of the leading 1 in the row above it.

Let's check this matrix:

1. The first row has a leading 1 at position (1,1). The second row has a leading 1 at position (2,3), so the leading entries are in the correct positions and satisfy the condition for leading 1s.
2. The column containing the leading 1 in the second row (third column) has no non-zero entries above it, which is correct.
3. There are no rows consisting entirely of zeroes.
4. The leading 1 in the second row is to the right of the leading 1 in the first row, so the staircase form condition is satisfied.

Therefore, **the matrix is in row-reduced echelon form (RREF)**.

The correct answer is: **a. Yes**

Would you like any further details or clarification?

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Here are 5 related questions:
1. What are the key differences between row echelon form and row-reduced echelon form?
2. Can every matrix be reduced to row-reduced echelon form?
3. How does Gaussian elimination differ from Gauss-Jordan elimination?
4. What is the significance of the number of pivots in a matrix?
5. How do you find the inverse of a matrix using row-reduced echelon form?

**Tip:** Always check each column with a leading 1 to ensure there are no other non-zero entries in that column when determining row-reduced echelon form.

Given the following matrix, is it in row reduced form? Matrix: 
[ [1, 1, 0, -5], [0, 0, 1, 3] ]

Learn how to determine if a 2x4 matrix is in row-reduced echelon form (RREF). This problem covers key concepts in linear algebra, including checking for leading 1s, zeroes in columns, and staircase form. Suitable for undergraduate students or advanced high school learners.

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