Questions: Write an augmented matrix for the following system of equations.
4x - 8y + 2z = -4
x - y + 9z = 6
5y - 6z = -2
The entries in the matrix are
Transcript text: Write an augmented matrix for the following system of equations.
\[
\begin{aligned}
4 x-8 y+2 z & =-4 \\
x-y+9 z & =6 \\
5 y-6 z & =-2
\end{aligned}
\]
$\square$ $\square$ $\square$ $\square$
The entries in the matrix are $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$
Solution
Solution Steps
Step 1: Identify Variables and Equations
We have 3 equations and 3 variables.
Step 2: Arrange Coefficients
The coefficients are arranged in the following order across all equations.
Step 3: Include Constant Terms
Each equation has a constant term on the right side of the equation.
Step 4: Form Augmented Matrix
The augmented matrix for the system is:
[4, -8, 2] | -4
[1, -1, 9] | 6
[0, 5, -6] | -2
Step 5: Adjust for Missing Variables
If there were any missing variables, we would insert 0s in their places. Assuming all variables are present.
Final Answer:
The augmented matrix representing the system of linear equations is:
4 -8 2 | -4
1 -1 9 | 6
0 5 -6 | -2