To find the reduced row echelon form (RREF) of the matrix \( A = \begin{bmatrix} 1 & 2 & -1 & 4 \end{bmatrix} \), we first note that this is a single row matrix.
Since the matrix has only one row, the row is already in echelon form. To convert it into reduced row echelon form, we need to ensure that the leading entry (the first non-zero number from the left in a non-zero row) is 1 and that all other entries in the column containing this leading 1 are zeros.
We start with our matrix:
\[ A = \begin{bmatrix} 1 & 2 & -1 & 4 \end{bmatrix} \]
- The first element in the row is already 1.
- To create zeros in the entries below (although there are no rows below in this case, we can view it as the form of a "complete" matrix):
Since we only have one row, the RREF is simply to make sure that this entry is 1. We don't need to make any other changes, and we can leave the row as it is:
The RREF of matrix \( A \) is:
\[ \text{RREF}(A) = \begin{bmatrix} 1 & 2 & -1 & 4 \end{bmatrix} \]
This is already in the reduced row echelon form.
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