Solve the system using Gaussian elimination or Gauss-Jordan elimination.
-$$\begin{array} { l }
- 2 x - y + 3 z = 13 \
x - 3 y - 3 z = - 4
\end{array}$$
A) $\{ ( - 1 , - 2,3 ) \}$
B) $\left\{ \left( \frac { 12 } { 7 } z - \frac { 43 } { 7 } , - \frac { 3 } { 7 } z - \frac { 5 } { 7 } , z \right) \mid z \right.$ is any real number $\}$
C){}
D) $\{ ( 1,2 , - 3 ) \}$

Question

Solve the system using Gaussian elimination or Gauss-Jordan elimination.
-$$\begin{array} { l } 
- 2 x - y + 3 z = 13 \
x - 3 y - 3 z = - 4
\end{array}$$
A) $\{ ( - 1 , - 2,3 ) \}$
B) $\left\{ \left( \frac { 12 } { 7 } z - \frac { 43 } { 7 } , - \frac { 3 } { 7 } z - \frac { 5 } { 7 } , z \right) \mid z \right.$ is any real number $\}$
C){}
D) $\{ ( 1,2 , - 3 ) \}$

Quizplus · Accepted Answer

This system of equations has two equations and three unknowns, which means it's underdetermined and will have infinitely many solutions, typically parameterized by one of the variables. By applying Gaussian elimination, we can simplify the system to express two of the variables in terms of the third. The correct answer reflects this, showing x and y in terms of z, indicating that for any real value of z, there's a corresponding solution for x and y.

Solve the System Using Gaussian Elimination or Gauss-Jordan Elimination −2x−y+3z=13x−3y−3z=−4\begin{array} { l } - 2 x - y + 3 z = 13 \\x - 3 y - 3 z = - 4\end{array}−2x−y+3z=13x−3y−3z=−4​

Solve the System Using Gaussian Elimination or Gauss-Jordan Elimination $\begin{array} { l } - 2 x - y + 3 z = 13 \\x - 3 y - 3 z = - 4\end{array}$