Schofield Hobbs
08/10/2024 · Middle School
Write the system of equations corresponding to the augmented matrix. Then perform the row operations \( R_{2}=-4 r_{1}+r_{2} \) and \( R_{3}=6 r_{1}+r_{3} \) on the given augmented \( \left[\begin{array}{rrr|r}1 & -2 & 4 & -5 \\ 4 & -4 & 4 & -5 \\ -6 & -7 & 2 & 4\end{array}\right] \) matrix. Perform the row operations \( R_{2}=-4 r_{1}+r_{2} \) and \( R_{3}=6 r_{1}+r_{3} \) on the original matrix given in the problem, and enter the resulting matrix below. \( \square \) \( \square \)
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The resulting matrix after the row operations is:
\[
\left[\begin{array}{rrr|r}
1 & -2 & 4 & -5 \\
0 & 4 & -12 & 15 \\
0 & -19 & 26 & -26
\end{array}\right]
\]
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