Use matrix inversion to solve the given system of linear equations. $\begin{aligned}
2 x - 3 y - 2 z & = 5 \
- z & = 1 \
x - 2 y + 2 z & = - 9
\end{aligned}$
A) $x = 29$ , $y = 16$ , $z = - 1$
B) $x = 26$ , $y = 17$ , $z = 1$
C) $x = 27$ , $y = 19$ , $z = 1$
D) $x = 27$ , $y = 17$ , $z = - 1$
E) The system is inconsistent.

Question

Use matrix inversion to solve the given system of linear equations.   $\begin{aligned}
2 x - 3 y - 2 z & = 5 \
- z & = 1 \
x - 2 y + 2 z & = - 9
\end{aligned}$  
A) $x = 29$ , $y = 16$ , $z = - 1$
B) $x = 26$ , $y = 17$ , $z = 1$
C) $x = 27$ , $y = 19$ , $z = 1$
D) $x = 27$ , $y = 17$ , $z = - 1$
E) The system is inconsistent.

Quizplus · Accepted Answer

The matrix form of the system is $AX = B$, where $A = \begin{bmatrix} 2 & -3 & -2 \ 0 & 0 & -1 \ 1 & -2 & 2 \end{bmatrix}$, $X = \begin{bmatrix} x \ y \ z \end{bmatrix}$, and $B = \begin{bmatrix} 5 \ 1 \ -9 \end{bmatrix}$. Solving $X = A^{-1}B$ gives $x = 27$, $y = 17$, $z = -1$.

Use Matrix Inversion to Solve the Given System of Linear 2x−3y−2z=5−z=1x−2y+2z=−9\begin{aligned}2 x - 3 y - 2 z & = 5 \\- z & = 1 \\x - 2 y + 2 z & = - 9\end{aligned}2x−3y−2z−zx−2y+2z​=5=1=−9​

Use Matrix Inversion to Solve the Given System of Linear $\begin{aligned}2 x - 3 y - 2 z & = 5 \\- z & = 1 \\x - 2 y + 2 z & = - 9\end{aligned}$