Write the system as a vector equation or matrix equation as indicated.
-Write the following system as a vector equation involving a linear combination of vectors. $$\begin{array} { l }
6 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 5 \
6 x _ { 1 } + 3 x _ { 3 } = - 5
\end{array}$$
A) $x _ { 1 } \left[ \begin{array} { l } 6 \ 6 \end{array} \right] + x _ { 2 } \left[ \begin{array} { r } - 6 \ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { c } - 1 \ 3 \end{array} \right] = \left[ \begin{array} { r } 5 \ - 5 \end{array} \right]$

B) $x _ { 1 } \left[ \begin{array} { c } 6 \ 6 \ - 1 \end{array} \right] + x _ { 2 } \left[ \begin{array} { c } 6 \ 0 \ 3 \end{array} \right] = \left[ \begin{array} { c } 5 \ - 5 \ 0 \end{array} \right]$

C) $6 \left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \end{array} \right] - 6 \left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \end{array} \right] - \left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \end{array} \right] = \left[ \begin{array} { r } 5 \ - 5 \ 0 \end{array} \right]$

D) $x _ { 1 } \left[ \begin{array} { l } 6 \ 6 \end{array} \right] + x _ { 2 } \left[ \begin{array} { r } - 6 \ 1 \end{array} \right] + x _ { 3 } \left[ \begin{array} { c } 1 \ 3 \end{array} \right] = \left[ \begin{array} { r } 5 \ - 5 \end{array} \right]$

Question

Write the system as a vector equation or matrix equation as indicated.
-Write the following system as a vector equation involving a linear combination of vectors. $$\begin{array} { l } 
6 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 5 \
6 x _ { 1 } + 3 x _ { 3 } = - 5
\end{array}$$
A) $x _ { 1 } \left[ \begin{array} { l } 6 \ 6 \end{array} \right] + x _ { 2 } \left[ \begin{array} { r } - 6 \ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { c } - 1 \ 3 \end{array} \right] = \left[ \begin{array} { r } 5 \ - 5 \end{array} \right]$

B) $x _ { 1 } \left[ \begin{array} { c } 6 \ 6 \ - 1 \end{array} \right] + x _ { 2 } \left[ \begin{array} { c } 6 \ 0 \ 3 \end{array} \right] = \left[ \begin{array} { c } 5 \ - 5 \ 0 \end{array} \right]$

C) $6 \left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \end{array} \right] - 6 \left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \end{array} \right] - \left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \end{array} \right] = \left[ \begin{array} { r } 5 \ - 5 \ 0 \end{array} \right]$

D) $x _ { 1 } \left[ \begin{array} { l } 6 \ 6 \end{array} \right] + x _ { 2 } \left[ \begin{array} { r } - 6 \ 1 \end{array} \right] + x _ { 3 } \left[ \begin{array} { c } 1 \ 3 \end{array} \right] = \left[ \begin{array} { r } 5 \ - 5 \end{array} \right]$

Quizplus · Accepted Answer

The correct vector equation is formed by grouping the coefficients of $x_1$, $x_2$, and $x_3$ from each equation into vectors, and setting these equal to the vector on the right-hand side of the equation. This matches option A, where each coefficient correctly corresponds to its variable across the two equations.

Write the System as a Vector Equation or Matrix Equation 6x1−6x2−x3=56x1+3x3=−5\begin{array} { l } 6 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 5 \\6 x _ { 1 } + 3 x _ { 3 } = - 5\end{array}6x1​−6x2​−x3​=56x1​+3x3​=−5​

Write the System as a Vector Equation or Matrix Equation $\begin{array} { l } 6 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 5 \\6 x _ { 1 } + 3 x _ { 3 } = - 5\end{array}$