In Exercises 5-6 an elementary matrix E and a matrix A are given. Identify the row operation corresponding to E and verify that the product E A results from applying the row operation to A .>(a) $E=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right], \quad A=\left[\begin{array}{rrrr}-1 & -2 & 5 & -1 \\ 3 & -6 & -6 & -6\end{array}\right]$
(b) $E=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & -3 & 1\end{array}\right], \quad A=\left[\begin{array}{rrrrr}2 & -1 & 0 & -4 & -4 \\ 1 & -3 & -1 & 5 & 3 \\ 2 & 0 & 1 & 3 & -1\end{array}\right]$
(c) $E=\left[\begin{array}{lll}1 & 0 & 4 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right], \quad A=\left[\begin{array}{ll}1 & 4 \\ 2 & 5 \\ 3 & 6\end{array}\right]$
In Exercises 5-6 an elementary matrix $E$ and a matrix $A$ are given. Identify the row operation corresponding to $E$ and verify that the product $E A$ results from applying the row operation to $A$.
(a) $E=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right], \quad A=\left[\begin{array}{rrrr}-1 & -2 & 5 & -1 \\ 3 & -6 & -6 & -6\end{array}\right]$ (b) $E=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & -3 & 1\end{array}\right], \quad A=\left[\begin{array}{rrrrr}2 & -1 & 0 & -4 & -4 \\ 1 & -3 & -1 & 5 & 3 \\ 2 & 0 & 1 & 3 & -1\end{array}\right]$ (c) $E=\left[\begin{array}{lll}1 & 0 & 4 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right], \quad A=\left[\begin{array}{ll}1 & 4 \\ 2 & 5 \\ 3 & 6\end{array}\right]$