Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$\left\{ \begin{array} { r l r }
3 x + 2 y - z + w & = 0 \
x - y + 4 z - w & = 28 \
- 2 x + y + 2 z - w & = 3 \
x + y + z + w & = 8
\end{array} \right.$$
A)(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)

Question

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. ​​ $$\left\{ \begin{array} { r l r } 
3 x + 2 y - z + w & = 0 \
x - y + 4 z - w & = 28 \
- 2 x + y + 2 z - w & = 3 \
x + y + z + w & = 8
\end{array} \right.$$ ​
A)​(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)

Quizplus · Accepted Answer

Using Gaussian elimination, we can convert the augmented matrix into row echelon form and solve for the variables. The row echelon form of the augmented matrix is:
\begin{bmatrix} 1 & -\frac{2}{3} & 2 & -\frac{1}{3} & -3 \ 0 & 1 & \frac{5}{2} & \frac{5}{2} & 5 \ 0 & 0 & 1 & 1 & 3 \end{bmatrix}
From this, we can see that x = 3, y = -2, z = 6, and w = 1. Therefore, the solution to the system of equations is (3,-2,6,1).

Use Matrices to Solve the System of Equations (If Possible)