Consider this Reduced-Row Echelon Form (RREF) of the augmented matrix of a system of linear
equations:

In the entry boxes provided below, enter the solutions for variables and in terms of
variables and (one digit per box), where you will need to determine the coefficients of
and and any constant value. Please do not use any space or comma in the answers you
enter.

Ask by Moran Stuart. in the United States

Jan 27,2025

Question

Consider this Reduced-Row Echelon Form (RREF) of the augmented matrix of a system of linear
equations:

In the entry boxes provided below, enter the solutions for variables and in terms of
variables and (one digit per box), where you will need to determine the coefficients of
and and any constant value. Please do not use any space or comma in the answers you
enter.

Ask by Moran Stuart. in the United States

Jan 27,2025

UpStudy AI · Accepted Answer

Given the Reduced-Row Echelon Form (RREF) of the augmented matrix:

$$
\left[\begin{array}{cccc:c}
1 & 0 & -1 & -4 & -14000 \
0 & 1 & 2 & 5 & 200000
\end{array}\right]
$$

We can interpret this as a system of linear equations:

1. $$ x_1 - x_3 - 4x_4 = -14000 $$
2. $$ x_2 + 2x_3 + 5x_4 = 200000 $$

To express $$ x_1 $$ and $$ x_2 $$ in terms of $$ x_3 $$ and $$ x_4 $$:

1. **Solving for $$ x_1 $$:**
   $$
   x_1 = x_3 + 4x_4 - 14000
   $$
   
2. **Solving for $$ x_2 $$:**
   $$
   x_2 = -2x_3 - 5x_4 + 200000
   $$

**Final Solutions:**

- $$ x_1 = x_3 + 4x_4 - 14000 $$
- $$ x_2 = -2x_3 - 5x_4 + 200000 $$

Please enter the solutions in the respective boxes without spaces or commas:

- **For $$ x_1 $$:** `1x3+4x4-14000`
- **For $$ x_2 $$:** `-2x3-5x4+200000`
- $$ x_1 = 1x_3 + 4x_4 - 14000 $$ - $$ x_2 = -2x_3 - 5x_4 + 200000 $$