- Is the matrix below in reduced row-echelon form? Why or why
not?
\begin{equation*}
\begin{bmatrix}
1 & 5 & 0 & 6 & 8\\
0 & 0 & 1 & 2 & 0\\
0 & 0 & 0 & 0 & 1
\end{bmatrix}
\end{equation*}
- Use row operations to convert the matrix below to reduced
row-echelon form and report the final matrix.
\begin{equation*}
\begin{bmatrix}
2 & 1 & 8\\
-1 & 1 & -1\\
-2 & 5 & 4
\end{bmatrix}
\end{equation*}
- Find all the solutions to the system below by using an augmented
matrix and row operations. Report your final matrix in reduced row-echelon form and the set of solutions.
\begin{align*}
2x_1 + 3x_2 - x_3&= 0\\
x_1 + 2x_2 + x_3&= 3\\
x_1 + 3x_2 + 3x_3&= 7
\end{align*}