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.) \[ (x, y)=(\square) \]
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Solution

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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 [120001]\left[\begin{array}{cc|c}1 & -2 & 0 \\ 0 & 0 & 1\end{array}\right] corresponds to the equations x2y=0x - 2y = 0 and 0=10 = 1. The second equation 0=10 = 1 is a contradiction, indicating that the system has no solution.

Step 1: Interpret the Matrix as a System of Equations

The given matrix [120001]\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 x2y=0x - 2y = 0. The second row corresponds to the equation 0=10 = 1.

Step 2: Analyze the System of Equations

The equation 0=10 = 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

DNE\boxed{\text{DNE}}

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