Question

Which option accurately represents the equation for the first row of the following augmented matrix?

⎡⎣⎢⎢3–230–14–36–19–410⎤⎦⎥⎥
[
3
0
–
3
9
–
2
–
1
6
–
4
3
4
–
1
10
]


(1 point)
Responses

3x+3z=9
3
𝑥
+
3
𝑧
=
9
3 x plus 3 z is equal to 9 - no response given

3x−3z=9
3
𝑥
−
3
𝑧
=
9
3 x minus 3 z is equal to 9 - no response given

3x+y−3z=9
3
𝑥
+
𝑦
−
3
𝑧
=
9
3 x plus y minus 3 z is equal to 9 - no response given

3x−3y=9

Answer 1

To determine the equation that corresponds to the first row of the given augmented matrix, we first need to identify the entries of the first row in the matrix. The augmented matrix is presented as:

\[
\begin{bmatrix}
3 & 0 & -3 & | & 9 \\
-2 & -1 & 6 & | & -4 \\
3 & 4 & -1 & | & 10
\end{bmatrix}
\]

The first row can be expressed in the form of an equation represented by:

\[ 3x + 0y - 3z = 9 \]

Since \(0y\) does not contribute to the equation, we can simplify this to:

\[ 3x - 3z = 9 \]

This matches the option:

3x−3z=9

So, the accurate representation of the equation for the first row of the augmented matrix is:

**3x−3z=9**