Solve the system of equations using Gauss-Jordan row reduction.
$$\begin{aligned}
x + y + z + u + v & = 30 \
y - z + u - v & = - 1 \
z + u + v & = 16 \
u - v & = - 2 \
v & = 7
\end{aligned}$$
A) $( - 3,33,18 , - 9,7 )$
B) $( 13,1,4,5,7 )$
C) $( 9,5,4,5,7 )$
D) inconsistent
E) dependent

Question

Solve the system of equations using Gauss-Jordan row reduction. 
  $$\begin{aligned}
x + y + z + u + v & = 30 \
y - z + u - v & = - 1 \
z + u + v & = 16 \
u - v & = - 2 \
v & = 7
\end{aligned}$$ 
A) $( - 3,33,18 , - 9,7 )$
B)   $( 13,1,4,5,7 )$
C)   $( 9,5,4,5,7 )$
D) inconsistent
E) dependent

Quizplus · Accepted Answer

Given $v = 7$, we can substitute this into the other equations to find the values of $u$, $z$, $y$, and $x$. Starting from the bottom, $u - v = -2$ becomes $u - 7 = -2$, so $u = 5$. Next, $z + u + v = 16$ becomes $z + 5 + 7 = 16$, so $z = 4$. Then, $y - z + u - v = -1$ becomes $y - 4 + 5 - 7 = -1$, so $y = 5$. Finally, $x + y + z + u + v = 30$ becomes $x + 5 + 4 + 5 + 7 = 30$, so $x = 9$. Therefore, the solution is $(9, 5, 4, 5, 7)$.

Solve the System of Equations Using Gauss-Jordan Row Reduction x+y+z+u+v=30y−z+u−v=−1z+u+v=16u−v=−2v=7\begin{aligned}x + y + z + u + v & = 30 \\y - z + u - v & = - 1 \\z + u + v & = 16 \\u - v & = - 2 \\v & = 7\end{aligned}x+y+z+u+vy−z+u−vz+u+vu−vv​=30=−1=16=−2=7​

Solve the System of Equations Using Gauss-Jordan Row Reduction $\begin{aligned}x + y + z + u + v & = 30 \\y - z + u - v & = - 1 \\z + u + v & = 16 \\u - v & = - 2 \\v & = 7\end{aligned}$