Final answer:
The given matrix is not in reduced row-echelon form because the 1 in the fourth row is not the only non-zero number in its column, violating the required condition for RREF.
Step-by-step explanation:
The question—"Is the given matrix in reduced row-echelon form?"—pertains to the topic of linear algebra, more specifically to matrix operations. A matrix is in reduced row-echelon form (RREF) when it satisfies the following conditions:
- Each leading entry in a row is the only non-zero number in its column.
- The leading entry in each non-zero row after the first occurs to the right of the leading entry in the previous row.
- Rows with all zero elements, if any, are below rows having a non-zero element.
- The leading entry in any non-zero row is 1, and it is the only non-zero entry in its column.
Given the matrix:
[ 1 3 0 1 0 0 ]
[ 0 1 0 4 0 0 ]
[ 0 0 0 1 1 2 ]
[ 0 0 0 1 0 0 ]
This matrix is not in reduced row-echelon form. The third condition is violated since the 1 in the fourth row is not the only non-zero number in its column; there's also a 1 in the third row. To be in RREF, each leading 1 must be the only non-zero number in its column.