The following matrix is in reduced row echelon form.
Determine the solution of the corresponding system of linear
equations or state that the system is inconsistent.

The solution:

Note: If inconsistent, enter DNE for all answers. If there are
infinite number of solutions, enter and in terms of .

Ask by Mathis Harper. in the United States

Mar 27,2025

Question

The following matrix is in reduced row echelon form.
Determine the solution of the corresponding system of linear
equations or state that the system is inconsistent.

The solution:

Note: If inconsistent, enter DNE for all answers. If there are
infinite number of solutions, enter and in terms of .

Ask by Mathis Harper. in the United States

Mar 27,2025

UpStudy AI · Accepted Answer

To determine the solution of the system of linear equations represented by the given matrix in reduced row echelon form:

$$
\left[\begin{array}{lll|l}
1 & 0 & 10 & 1 \
0 & 1 & 14 & 6 \
0 & 0 & 0 & 1
\end{array}\right]
$$

we can interpret this matrix as a system of equations:

1. $$ x + 10z = 1 $$
2. $$ y + 14z = 6 $$
3. $$ 0 = 1 $$

The third equation $$ 0 = 1 $$ is a contradiction, indicating that the system is inconsistent.

Thus, the solution is:

$$
x = \text{DNE}
$$
$$
y = \text{DNE}
$$
$$
z = \text{DNE}
$$
The system is inconsistent, so there is no solution.