Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r }
1 & - 11 & - 13 & - 30 \
0 & - 14 & - 3 & 1 \
0 & 5 & - 9 & - 26
\end{array} \right]$$
What row operation would you perform next?
A) Multiply row 1 by $- \frac { 1 } { 11 }$.
B) Add $- 5$ times row 1 to $- 11$ times row 3 to obtain a zero in the third row, second column position.
C) Add row 1 to row $2 .$
D) Multiply row 2 by $- \frac { 1 } { 14 }$.

Question

Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r } 
1 & - 11 & - 13 & - 30 \
0 & - 14 & - 3 & 1 \
0 & 5 & - 9 & - 26
\end{array} \right]$$
What row operation would you perform next?
A) Multiply row 1 by $- \frac { 1 } { 11 }$.
B) Add $- 5$ times row 1 to $- 11$ times row 3 to obtain a zero in the third row, second column position.
C) Add row 1 to row $2 .$
D) Multiply row 2 by $- \frac { 1 } { 14 }$.

Quizplus · Accepted Answer

The goal in the Gauss-Jordan method is to transform the matrix into reduced row echelon form. The next logical step after obtaining zeros below the leading 1 in the first column is to create a leading 1 in the second row, second column. This can be achieved by multiplying row 2 by $-\frac{1}{14}$, as it directly transforms the leading entry of row 2 into 1.

Suppose That You Are Solving a System of Three Linear [1−11−13−300−14−3105−9−26]\left[ \begin{array} { r r r | r } 1 & - 11 & - 13 & - 30 \\0 & - 14 & - 3 & 1 \\0 & 5 & - 9 & - 26\end{array} \right]​100​−11−145​−13−3−9​−301−26​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { r r r | r } 1 & - 11 & - 13 & - 30 \\0 & - 14 & - 3 & 1 \\0 & 5 & - 9 & - 26\end{array} \right]$