Write the system of equations as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants.
-$$\begin{array} { l }
- 5 x - 8 y + 9 z = 16 \
2 x - z = 5 \
- 7 y + z = 8
\end{array}$$
A) $\left[ \begin{array} { l l l } 5 & 8 & 9 \ 2 & 0 & 1 \ 0 & 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } 16 \ 5 \ 8 \end{array} \right]$
B) $\left[ \begin{array} { r r r } - 5 & - 8 & 9 \ 2 & - 1 & 0 \ - 7 & 1 & 0 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } 16 \ 5 \ 8 \end{array} \right]$
C) $\left[ \begin{array} { r r r } - 5 & - 8 & 9 \ 2 & 0 & - 1 \ 0 & - 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } - 16 \ - 5 \ - 8 \end{array} \right]$
D) $\left[ \begin{array} { r r r } - 5 & - 8 & 9 \ 2 & 0 & - 1 \ 0 & - 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } 16 \ 5 \ 8 \end{array} \right]$

Question

Write the system of equations as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants.
-$$\begin{array} { l } 
- 5 x - 8 y + 9 z = 16 \
2 x - z = 5 \
- 7 y + z = 8
\end{array}$$
A) $\left[ \begin{array} { l l l } 5 & 8 & 9 \ 2 & 0 & 1 \ 0 & 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } 16 \ 5 \ 8 \end{array} \right]$
B) $\left[ \begin{array} { r r r } - 5 & - 8 & 9 \ 2 & - 1 & 0 \ - 7 & 1 & 0 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } 16 \ 5 \ 8 \end{array} \right]$
C) $\left[ \begin{array} { r r r } - 5 & - 8 & 9 \ 2 & 0 & - 1 \ 0 & - 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } - 16 \ - 5 \ - 8 \end{array} \right]$
D) $\left[ \begin{array} { r r r } - 5 & - 8 & 9 \ 2 & 0 & - 1 \ 0 & - 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { r } 16 \ 5 \ 8 \end{array} \right]$

Quizplus · Accepted Answer

The correct matrix equation is formed by aligning the coefficients of $x$, $y$, and $z$ from each equation into the matrix $A$, the variables $x$, $y$, and $z$ into the column matrix $X$, and the constants on the right side of the equations into the column matrix $B$. Option D correctly represents the system of equations given, with the coefficients and constants properly placed in their respective matrices.

Write the System of Equations as a Matrix Equation of the Form