Write the system of linear equations as a matrix equation, AX = B. $$\left\{ \begin{array} { l }
2 x _ { 1 } + 3 x _ { 2 } = 8 \
4 x _ { 1 } + 5 x _ { 2 } = 16
\end{array} \right.$$
A) $\left[ \begin{array} { l l }
2 & 3 \
4 & 5
\end{array} \right] \left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c }
8 \
16
\end{array} \right]$
B) $\left[ \begin{array} { l l }
2 & 4 \
3 & 5
\end{array} \right] \left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c }
8 \
16
\end{array} \right]$
C) $\left[ \begin{array} { l l }
2 & 3 \
4 & 5
\end{array} \right] \left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c }
- 8 \
- 16
\end{array} \right]$
D) $\left[ \begin{array} { c c }
2 & 8 \
4 & 16
\end{array} \right] \left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { l }
3 \
5
\end{array} \right]$
E) $\left[ \begin{array} { l l }
2 & 3 \
4 & 5
\end{array} \right] \left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c }
16 \
8
\end{array} \right]$

Question

Write the system of linear equations as a matrix equation, AX = B.   $$\left\{ \begin{array} { l } 
2 x _ { 1 } + 3 x _ { 2 } = 8 \
4 x _ { 1 } + 5 x _ { 2 } = 16
\end{array} \right.$$  
A) $\left[ \begin{array} { l l } 
2 & 3 \
4 & 5
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c } 
8 \
16
\end{array} \right]$
B) $\left[ \begin{array} { l l } 
2 & 4 \
3 & 5
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c } 
8 \
16
\end{array} \right]$
C) $\left[ \begin{array} { l l } 
2 & 3 \
4 & 5
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c } 
- 8 \
- 16
\end{array} \right]$
D) $\left[ \begin{array} { c c } 
2 & 8 \
4 & 16
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { l } 
3 \
5
\end{array} \right]$
E) $\left[ \begin{array} { l l } 
2 & 3 \
4 & 5
\end{array} \right] \left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 }
\end{array} \right] = \left[ \begin{array} { c } 
16 \
8
\end{array} \right]$

Quizplus · Accepted Answer

The matrix equation AX = B is formed by placing the coefficients of $x_1$ and $x_2$ in a matrix A, the variables $x_1$ and $x_2$ in a column matrix X, and the constants on the right-hand side of the equations in a column matrix B. Option A correctly represents this structure.

Write the System of Linear Equations as a Matrix Equation {2x1+3x2=84x1+5x2=16\left\{ \begin{array} { l } 2 x _ { 1 } + 3 x _ { 2 } = 8 \\4 x _ { 1 } + 5 x _ { 2 } = 16\end{array} \right.{2x1​+3x2​=84x1​+5x2​=16​

Write the System of Linear Equations as a Matrix Equation $\left\{ \begin{array} { l } 2 x _ { 1 } + 3 x _ { 2 } = 8 \\4 x _ { 1 } + 5 x _ { 2 } = 16\end{array} \right.$