Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { r }
w - x + 2 y + z = 1 \
x + y = 5 \
y - z = 4
\end{array}$$
A) No solution
B) $( - 10,0,5,1 )$
C) $( - 6,1,4 , z )$
D) $( - 6 - 4 z , 1 - z , 4 + z , z )$

Question

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { r } 
w - x + 2 y + z = 1 \
x + y = 5 \
y - z = 4
\end{array}$$
A) No solution
B) $( - 10,0,5,1 )$
C) $( - 6,1,4 , z )$
D) $( - 6 - 4 z , 1 - z , 4 + z , z )$

Quizplus · Accepted Answer

The system of equations can be represented as an augmented matrix and reduced to row echelon form. The presence of a parameter $z$ in the solution indicates that there are infinitely many solutions, depending on the value of $z$. The correct solution is $( - 6 - 4 z , 1 - z , 4 + z , z )$, which shows the relationship between the variables and the parameter $z$.

Solve the System of Equations by Finding the Reduced Row w−x+2y+z=1x+y=5y−z=4\begin{array} { r } w - x + 2 y + z = 1 \\x + y = 5 \\y - z = 4\end{array}w−x+2y+z=1x+y=5y−z=4​

Solve the System of Equations by Finding the Reduced Row $\begin{array} { r } w - x + 2 y + z = 1 \\x + y = 5 \\y - z = 4\end{array}$