Questions: The matrix [1 -2 0; 0 0 1] is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use y=t as the parameter. (If an answer does not exist, enter DNE.) (x, y)=( )

The matrix [1 -2 0; 0 0 1] is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations.
Write the solution as an ordered pair. For parametric solutions use y=t as the parameter. (If an answer does not exist, enter DNE.)
(x, y)=( )

Transcript text: The matrix $\left[\begin{array}{cc|c}1 & -2 & 0 \\ 0 & 0 & 1\end{array}\right]$ is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use $y=t$ as the parameter. (If an answer does not exist, enter DNE.) \[ (x, y)=(\square) \]

Solution

Solution Steps

To solve the system of linear equations represented by the given matrix in reduced row-echelon form, we need to interpret the matrix as a system of equations. The matrix $\left[\begin{array}{cc|c}1 & -2 & 0 \\ 0 & 0 & 1\end{array}\right]$ corresponds to the equations $x - 2y = 0$ and $0 = 1$. The second equation $0 = 1$ is a contradiction, indicating that the system has no solution.

Step 1: Interpret the Matrix as a System of Equations

The given matrix $\left[\begin{array}{cc|c}1 & -2 & 0 \\ 0 & 0 & 1\end{array}\right]$ represents a system of linear equations. The first row corresponds to the equation $x - 2y = 0$. The second row corresponds to the equation $0 = 1$.

Step 2: Analyze the System of Equations

The equation $0 = 1$ is a contradiction because it is not possible for zero to equal one. This indicates that the system of equations is inconsistent and has no solution.

Final Answer

$\boxed{\text{DNE}}$

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