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

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 $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$
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Solution

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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

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