A system of equations was written as an augmented matrix, which was row reduced to: $$ \left[\begin{array}{cccc}1 & 0 & 0 & -3 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & -1\end{array} ight] $$ What is the solution to the original system of equations? $$ x= $$ $$ y= $$ $$ z= $$

Question

A system of equations was written as an augmented matrix, which was row reduced to: $$ \left[\begin{array}{cccc}1 & 0 & 0 & -3 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & -1\end{array}ight] $$ What is the solution to the original system of equations? $$ x= $$ $$ y= $$ $$ z= $$

UpStudy AI · Accepted Answer

The given augmented matrix after row reduction is:

$$
\begin{bmatrix}
1 & 0 & 0 & -3 \
0 & 1 & 0 & 0 \
0 & 0 & 1 & -1
\end{bmatrix}
$$

This matrix corresponds to the following system of equations:

$$
\begin{cases}
1x + 0y + 0z = -3 \
0x + 1y + 0z = 0 \
0x + 0y + 1z = -1
\end{cases}
$$

Simplifying each equation:

1. $$ x = -3 $$
2. $$ y = 0 $$
3. $$ z = -1 $$

**Solution:**
$$
\boxed{
\begin{aligned}
x &= -3, \
y &= 0, \
z &= -1
\end{aligned}
}
$$
The solution to the original system of equations is: $$ x = -3, \quad y = 0, \quad z = -1 $$

A system of equations was written as an augmented matrix, which was row reduced to: \( \left[\begin{array}{cccc}1 & 0 & 0 & -3 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1\end{array}\right] \) What is the solution to the original system of equations? \( x= \) \( y= \) \( z= \)

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