Write the system of linear equations represented by the augmented matrix to the right Use $x, y$, and $z$ for the variables.
\[
\left[\begin{array}{rrr|r}
5 & 0 & 2 & -14 \\
0 & 1 & -4 & 11 \\
7 & 2 & 0 & 4
\end{array}\right]
\]
Write the equation represented by the first row.
\[
5 x+2 z=-14
\]
Write the equation represented by the second row.
Answer
Final Answer: \(\boxed{y - 4z = 11}\)
Step 1 ：Write the system of linear equations represented by the augmented matrix to the right Use \(x, y\), and \(z\) for the variables.
Step 2 ：Write the equation represented by the first row. \(5 x+2 z=-14\)
Step 3 ：Write the equation represented by the second row. The question asks for the equation represented by the second row of the given augmented matrix. The second row of the matrix is [0, 1, -4, 11]. This corresponds to the equation 0*x + 1*y - 4*z = 11. We can simplify this to \(y - 4z = 11\).
Step 4 ：Final Answer: \(\boxed{y - 4z = 11}\)
