Determine the first step in solving the system $\left\{ \begin{array} { l }
6 x + y - 6 z = - 3 \
8 x - 7 y - z = - 12 \
x - 5 y - 4 z = - 3
\end{array} \right.$ by matrices.
A) Multiply row 1 by $- 6$ .
B) Interchange rows 1 and 3.
C) Interchange rows 1 and 2.
D) Multiply row 2 by $\frac { 1 } { 8 }$ .

Question

Determine the first step in solving the system $\left\{ \begin{array} { l } 
6 x + y - 6 z = - 3 \
8 x - 7 y - z = - 12 \
x - 5 y - 4 z = - 3
\end{array} \right.$ by matrices.
A) Multiply row 1 by $- 6$ .
B) Interchange rows 1 and 3.
C) Interchange rows 1 and 2.
D) Multiply row 2 by $\frac { 1 } { 8 }$  .

Quizplus · Accepted Answer

Interchanging rows 1 and 3 places the equation with the smallest coefficient in front of $x$ at the top, simplifying the process of converting the system into an upper triangular matrix.

Determine the First Step in Solving the System {6x+y−6z=−38x−7y−z=−12x−5y−4z=−3\left\{ \begin{array} { l } 6 x + y - 6 z = - 3 \\8 x - 7 y - z = - 12 \\x - 5 y - 4 z = - 3\end{array} \right.⎩⎨⎧​6x+y−6z=−38x−7y−z=−12x−5y−4z=−3​

Determine the First Step in Solving the System $\left\{ \begin{array} { l } 6 x + y - 6 z = - 3 \\8 x - 7 y - z = - 12 \\x - 5 y - 4 z = - 3\end{array} \right.$