Form the augmented matrix for the system of linear equations below. ${6x+y+z=24x+4y+4z=98x+y+4z=−7\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.$

A) $[29−7]\left[ \begin{array} { c } 2 \\9 \\- 7\end{array} \right]$
B) $[648141144]\left[ \begin{array} { l l l } 6 & 4 & 8 \\1 & 4 & 1 \\1 & 4 & 4\end{array} \right]$
C) $[61124449814−7]\left[ \begin{array} { c c c c } 6 & 1 & 1 & 2 \\4 & 4 & 4 & 9 \\8 & 1 & 4 & - 7\end{array} \right]$
D) $[611444814]\left[ \begin{array} { l l l } 6 & 1 & 1 \\4 & 4 & 4 \\8 & 1 & 4\end{array} \right]$
E) $[64814114429−7]\left[ \begin{array} { c c c } 6 & 4 & 8 \\1 & 4 & 1 \\1 & 4 & 4 \\2 & 9 & - 7\end{array} \right]$

Question

Form the augmented matrix for the system of linear equations below.   { 6 x + y + z = 2 4 x + 4 y + 4 z = 9 8 x + y + 4 z = − 7 \left\{ \begin{array} { r } 6 x + y + z = 2 \4 x + 4 y + 4 z = 9 \8 x + y + 4 z = - 7\end{array} ight. ⎩ ⎨ ⎧ ​ 6 x + y + z = 2 4 x + 4 y + 4 z = 9 8 x + y + 4 z = − 7 ​ A)    [ 2 9 − 7 ] \left[ \begin{array} { c } 2 \9 \- 7\end{array} ight] ​ 2 9 − 7 ​ ​ B)    [ 6 4 8 1 4 1 1 4 4 ] \left[ \begin{array} { l l l } 6  &  4  &  8 \1  &  4  &  1 \1  &  4  &  4\end{array} ight] ​ 6 1 1 ​ 4 4 4 ​ 8 1 4 ​ ​ C)    [ 6 1 1 2 4 4 4 9 8 1 4 − 7 ] \left[ \begin{array} { c c c c } 6  &  1  &  1  &  2 \4  &  4  &  4  &  9 \8  &  1  &  4  &  - 7\end{array} ight] ​ 6 4 8 ​ 1 4 1 ​ 1 4 4 ​ 2 9 − 7 ​ ​ D)    [ 6 1 1 4 4 4 8 1 4 ] \left[ \begin{array} { l l l } 6  &  1  &  1 \4  &  4  &  4 \8  &  1  &  4\end{array} ight] ​ 6 4 8 ​ 1 4 1 ​ 1 4 4 ​ ​ E)    [ 6 4 8 1 4 1 1 4 4 2 9 − 7 ] \left[ \begin{array} { c c c } 6  &  4  &  8 \1  &  4  &  1 \1  &  4  &  4 \2  &  9  &  - 7\end{array} ight] ​ 6 1 1 2 ​ 4 4 4 9 ​ 8 1 4 − 7 ​ ​

Courtney Fraser · Accepted Answer

Final Answer : C, Explanation :   The augmented matrix for a system of linear equations is formed by arranging the coefficients of the variables and the constant terms in a rectangular array, with each equation forming a row. Therefore, the correct augmented matrix for the given system is: [ 6 1 1 2 4 4 4 9 8 1 4 − 7 ] \left[ \begin{array} { c c c c } 6  &  1  &  1  &  2 \4  &  4  &  4  &  9 \8  &  1  &  4  &  - 7\end{array} ight] ​ 6 4 8 ​ 1 4 1 ​ 1 4 4 ​ 2 9 − 7 ​ ​ Choice C is the only option that matches this augmented matrix.

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