Given
The matrix,

To find:
The solution to the system of equation.
Step-by-step explanation:
It is given that,

That implies,
Consider,
![\begin{gathered} [A|B]=\begin{bmatrix}{1} & 1{} & {1} & {|\text{ }4} \\ {-2} & {3} & {3} & {|\text{ }2} \\ {1} & {2} & {3} & {|\text{ }5} \\ {} & {} & {} & {}\end{bmatrix} \\ \approx\begin{bmatrix}{1} & 1{} & {1} & {|\text{ }4} \\ {0} & 5 & {5} & |\text{ }10 \\ 0 & 1 & 2 & {|\text{ }1} \\ {} & {} & {} & {}\end{bmatrix}[R_2=R_2+2R_1,\text{ }R_3=R_3-R_1] \\ \approx\begin{bmatrix}{1} & 1{} & {1} & {|\text{ }4} \\ {0} & 5 & {5} & |\text{ }10 \\ 0 & 0 & 5 & {|\text{ }-5} \\ {} & {} & {} & {}\end{bmatrix}[R_3=5R_3-R_2] \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/hs6zrxsj3nuh2l7lrc8vyqaodocaj6j4dw.png)
Therefore,

Then, (3) implies,

Substitute z = -1 in (2).
Then,

Substitute y = 3, z = -1 in (1).
Then,

Hence, the solution is, option B) x = 2, y = 3, z = -1.