Question

Write the augmented matrix for the following system of equations.
minus, 4, minus, 2, z, equals, minus, y
−4−2z=
−y
minus, 3, y, plus, 2, z, equals, minus, 2
−3y+2z=
−2
z, minus, 9, y, equals, minus, 8, x
z−9y=
−8x

Answer 1

To write the augmented matrix for the given system of equations, we need to rearrange the equations based on the standard form \(Ax + By + Cz = D\).

Let's first rewrite the equations so that they all have \(x\), \(y\), and \(z\) on the left and the constants on the right.

1. From the equation \( -4 - 2z = -y \):
- Rearranging gives us \(0x + y - 2z = -4\).

2. From the equation \( -3y + 2z = -2 \):
- This can be rearranged to \(0x - 3y + 2z = -2\).

3. From the equation \( z - 9y = -8x \):
- Rearranging gives us \(8x - 9y + z = 0\).

Now, we can represent the coefficients of \(x\), \(y\), and \(z\) along with the constants in the augmented matrix form.

The augmented matrix for this system of equations is:

\[
\begin{bmatrix}
0 & 1 & -2 & | & -4 \\
0 & -3 & 2 & | & -2 \\
8 & -9 & 1 & | & 0
\end{bmatrix}
\]

Here, the vertical line separates the coefficients from the constants. Each row of the matrix corresponds to one of the equations in the system.