Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\begin{array} { l }
x - y + 2 z + w = 2 \
y + z = 2 \
z - w = 3
\end{array}$$

A) $\varnothing$
B) $\{ ( - 9 , - 2,4,1 ) \}$
C)$\{(-5-4 \mathrm{w},-1-\mathrm{w}, 3+\mathrm{w}, \mathrm{w})\}$
D) $\{ ( - 5 , - 1,3 , \mathrm { w } ) \}$

Question

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\begin{array} { l } 
x - y + 2 z + w = 2 \
y + z = 2 \
z - w = 3
\end{array}$$

A) $\varnothing$
B) $\{ ( - 9 , - 2,4,1 ) \}$
C)$\{(-5-4 \mathrm{w},-1-\mathrm{w}, 3+\mathrm{w}, \mathrm{w})\}$
D) $\{ ( - 5 , - 1,3 , \mathrm { w } ) \}$

Quizplus · Accepted Answer

The system of equations is consistent and has infinitely many solutions. Solving using matrices and row operations, we find the solution set in terms of the parameter $ w $.

Solve Each System of Equations Using Matrices (Row Operations) x−y+2z+w=2y+z=2z−w=3\begin{array} { l } x - y + 2 z + w = 2 \\y + z = 2 \\z - w = 3\end{array}x−y+2z+w=2y+z=2z−w=3​

Solve Each System of Equations Using Matrices (Row Operations) $\begin{array} { l } x - y + 2 z + w = 2 \\y + z = 2 \\z - w = 3\end{array}$