Provide an appropriate response.
-Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix.
$$\left[ \begin{array} { r r r | r }
1 & - 15 & 7 & 19 \
0 & 1 & 14 & - 8 \
0 & - 9 & 20 & - 2
\end{array} \right]$$
What row transformation would you perform next?
A) Multiply row 3 by $\frac { 1 } { 20 }$.
B) Add 9 times row 1 to $- 15$ times row 3 .
C) Add $- \frac { 1 } { a }$ times row 2 to row 3 .
D) Add 9 times row 2 to row 3 .

Question

Provide an appropriate response.
-Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix.
$$\left[ \begin{array} { r r r | r } 
1 & - 15 & 7 & 19 \
0 & 1 & 14 & - 8 \
0 & - 9 & 20 & - 2
\end{array} \right]$$
What row transformation would you perform next?
A) Multiply row 3 by $\frac { 1 } { 20 }$.
B) Add 9 times row 1 to $- 15$ times row 3 .
C) Add $- \frac { 1 } { a }$ times row 2 to row 3 .
D) Add 9 times row 2 to row 3 .

Quizplus · Accepted Answer

The goal in the Gauss-Jordan method is to make the matrix into reduced row echelon form. This involves making the entries below and above the leading 1s to be 0. Since the second row has a leading 1 in the second column, adding 9 times the second row to the third row will make the second column of the third row zero, which is the next step in achieving reduced row echelon form.

Provide an Appropriate Response [1−157190114−80−920−2]\left[ \begin{array} { r r r | r } 1 & - 15 & 7 & 19 \\0 & 1 & 14 & - 8 \\0 & - 9 & 20 & - 2\end{array} \right]​100​−151−9​71420​19−8−2​​

Provide an Appropriate Response $\left[ \begin{array} { r r r | r } 1 & - 15 & 7 & 19 \\0 & 1 & 14 & - 8 \\0 & - 9 & 20 & - 2\end{array} \right]$