Suppose that you are solving a system of three linear equations in three variables by the row echelon method ans obtain the following augmented matrix.
$$\left[ \begin{array} { l r r r }
1 & - 12 & - 18 & 12 \
0 & 1 & - 5 & 10 \
0 & - 20 & - 11 & 3
\end{array} \right]$$
What row transformation would you perform next?
A) Add 20 times row 1 to $- 12$ times row 3 .
B) Multiply row 3 by $- \frac { 1 } { 11 }$.
C) Add $- \frac { 1 } { 20 }$ times row 2 to row 3 .
D) Add 20 times row 2 to row $3 .$

Question

Suppose that you are solving a system of three linear equations in three variables by the row echelon method ans obtain the following augmented matrix.
$$\left[ \begin{array} { l r r r } 
1 & - 12 & - 18 & 12 \
0 & 1 & - 5 & 10 \
0 & - 20 & - 11 & 3
\end{array} \right]$$
What row transformation would you perform next?
A) Add 20 times row 1 to $- 12$ times row 3 .
B) Multiply row 3 by $- \frac { 1 } { 11 }$.
C) Add $- \frac { 1 } { 20 }$ times row 2 to row 3 .
D) Add 20 times row 2 to row $3 .$

Quizplus · Accepted Answer

The goal in the row echelon method is to create zeros below the leading entries in each column. Since the second row has a leading 1 in the second column, adding 20 times row 2 to row 3 will create a zero in the third row, second column, which is the next step in achieving row echelon form.

Suppose That You Are Solving a System of Three Linear [1−12−181201−5100−20−113]\left[ \begin{array} { l r r r } 1 & - 12 & - 18 & 12 \\0 & 1 & - 5 & 10 \\0 & - 20 & - 11 & 3\end{array} \right]​100​−121−20​−18−5−11​12103​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { l r r r } 1 & - 12 & - 18 & 12 \\0 & 1 & - 5 & 10 \\0 & - 20 & - 11 & 3\end{array} \right]$