Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 24: 53

Reduced row-echelon matrix that is row-equivalent to the given matrix is: \begin{bmatrix} 1&0 \\ 0&1 \end{bmatrix}

Apply elementary row operations to find the reduced row-echelon matrix that is row-equivalent to the given matrix: \begin{bmatrix} 1&2 \\ -1&2 \end{bmatrix} $R_{1}+R_{2} \to R_{2}$ \begin{bmatrix} 1&2 \\ 0&4 \end{bmatrix} $ \frac{1}{4} R_{2} \to R_{2}$ \begin{bmatrix} 1&2 \\ 0&1 \end{bmatrix} $-2R_{2} + R_{1} \to R_{2}$ \begin{bmatrix} 1&0 \\ 0&1 \end{bmatrix}