Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x+2y-3z=5\\
x-y+2z=8\\
3x+5y-8z=-2
\end{cases}$
The augmented matrix associated with the system is:
$A=\begin{bmatrix}2&2&-3&|&5\\1&-1&2&|&8\\3&5&-8&|&-2\end{bmatrix}$
Multiply $R_2$ by -1 and add it to $R_1$:
$\begin{bmatrix}1&3&-5&|&-3\\1&-1&2&|&8\\3&5&-8&|&-2\end{bmatrix}$
Multiply $R_1$ by -1 and add it to $R_2$:
$\begin{bmatrix}1&3&-5&|&-3\\0&-4&7&|&11\\3&5&-8&|&-2\end{bmatrix}$
Multiply $R_1$ by -3 and add it to $R_3$:
$\begin{bmatrix}1&3&-5&|&-3\\0&-4&7&|&11\\0&-4&7&|&7\end{bmatrix}$
Multiply $R_2$ by -1 and add it to $R_3$:
$\begin{bmatrix}1&3&-5&|&-3\\0&-4&7&|&11\\0&0&0&|&-4\end{bmatrix}$
Multiply $R_2$ by $-\dfrac{1}{4}$:
$\begin{bmatrix}1&3&-5&|&-3\\0&1&-\dfrac{7}{4}&|&-\dfrac{11}{4}\\0&0&0&|&-4\end{bmatrix}$
As the last line contains only zeros to the left of the bar and a non zero element to the right, the system is inconsistent.
