Write the system of linear equations as a matrix equation $A X = B$, and use Gauss-Jordan elimination on the augmented matrix $[ A \vdots B ]$ to solve for the matrix $X$.
$$\left\{ \begin{aligned}
x _ { 1 } + 6 x _ { 2 } + 9 x _ { 3 } & = - 44 \
- 7 x _ { 1 } + 2 x _ { 2 } - x _ { 3 } & = - 54 \
8 x _ { 1 } + 3 x _ { 2 } + 6 x _ { 3 } & = 26
\end{aligned} \right.$$
A) $X = \left[ \begin{array} { l } 28 \ 12 \ 21 \end{array} \right]$
B) $X = \left[ \begin{array} { c } 12 \ - 7 \ - 4 \end{array} \right]$
C) $X = \left[ \begin{array} { c } 7 \ - 4 \ - 3 \end{array} \right]$
D) $X = \left[ \begin{array} { l } - 12 \ - 28 \ - 21 \end{array} \right]$
E) $X = \left[ \begin{array} { c } - 7 \ 3 \ - 4 \end{array} \right]$

Question

Quizplus · Accepted Answer

The correct solution can be found by transforming the augmented matrix $[A|B]$ using Gauss-Jordan elimination. The steps involve row operations to get the matrix in reduced row echelon form (RREF), from which the solution $X$ can be directly read off. The solution $X = \left[ \begin{array} { c } 7 \ - 4 \ - 3 \end{array} \right]$ indicates that after performing these operations, the values of $x_1, x_2,$ and $x_3$ are 7, -4, and -3, respectively, which satisfies the given system of equations.

Write the System of Linear Equations as a Matrix Equation AX=BA X = BAX=B

Write the System of Linear Equations as a Matrix Equation $A X = B$