Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r }
1 & 7 & - 4 & 9 \
0 & 1 & 20 & 4 \
0 & 8 & 6 & - 9
\end{array} \right]$$
What row transformation would you perform next?
A) Multiply row 3 by $\frac { 1 } { 6 }$.
B) Add $- 8$ times row 1 to 7 times row 3 .
C) Add $- 8$ times row 2 to row 3 .
D) Add $\frac { 1 } { 8 }$ times row 2 to row 3 .

Question

Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r } 
1 & 7 & - 4 & 9 \
0 & 1 & 20 & 4 \
0 & 8 & 6 & - 9
\end{array} \right]$$
What row transformation would you perform next?
A) Multiply row 3 by $\frac { 1 } { 6 }$.
B) Add $- 8$ times row 1 to 7 times row 3 .
C) Add $- 8$ times row 2 to row 3 .
D) Add $\frac { 1 } { 8 }$ times row 2 to row 3 .

Quizplus · Accepted Answer

The goal in the Gauss-Jordan method is to transform the matrix into reduced row echelon form (RREF), where each leading entry of a row is 1 and is the only nonzero entry in its column. After making the second row's leading entry a 1, the next step is to eliminate the 8 below this leading 1 in the second row to move towards RREF. This is achieved by adding -8 times the second row to the third row, which corresponds to option C.

Suppose That You Are Solving a System of Three Linear [17−4901204086−9]\left[ \begin{array} { r r r | r } 1 & 7 & - 4 & 9 \\0 & 1 & 20 & 4 \\0 & 8 & 6 & - 9\end{array} \right]​100​718​−4206​94−9​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { r r r | r } 1 & 7 & - 4 & 9 \\0 & 1 & 20 & 4 \\0 & 8 & 6 & - 9\end{array} \right]$