Question

write the augmented matrix for the system of equations to the right.
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$$\begin{cases} \\begin{align*} x - 3y + 2z &= -3\\\\ 6x - 3y &= 7\\\\ x - 3z &= -5 \\end{align*} \\end{cases}$$

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enter each element.
$\

$$\begin{bmatrix}\\square & \\square & \\square & \\mid & \\square\\\\\\square & \\square & \\square & \\mid & \\square\\\\\\square & \\square & \\square & \\mid & \\square\\end{bmatrix}$$

$
(do not simplify.)

Explanation:

Step1: Identify coefficients for each equation

For $x - 3y + 2z = -3$: coefficients are $1, -3, 2$; constant is $-3$
For $6x - 3y = 7$: coefficients are $6, -3, 0$; constant is $7$
For $x - 3z = -5$: coefficients are $1, 0, -3$; constant is $-5$

Step2: Assemble augmented matrix

Arcoefficients and constants into rows:

$$\begin{bmatrix} 1 & -3 & 2 & \bigm| & -3 \\ 6 & -3 & 0 & \bigm| & 7 \\ 1 & 0 & -3 & \bigm| & -5 \end{bmatrix}$$

Answer:

$$\begin{bmatrix} 1 & -3 & 2 & \bigm| & -3 \\ 6 & -3 & 0 & \bigm| & 7 \\ 1 & 0 & -3 & \bigm| & -5 \end{bmatrix}$$