Write the augmented matrix for the system of linear equations.

Question

3 x plus y plus 4 z
equals
9
2 x minus 6 y minus z
equals
4
x minus 7 y minus 6 z
equals
negative 9
Question content area bottom
Part 1
Enter the augmented matrix.

Answer 1

To write the augmented matrix for the given system of linear equations, we first represent the coefficients of the variables \(x\), \(y\), and \(z\) along with the constants from the right-hand side of the equations.

The given system of equations is:

1. \(3x + 1y + 4z = 9\)
2. \(2x - 6y - 1z = 4\)
3. \(1x - 7y - 6z = -9\)

We will now create the augmented matrix, which is formed by placing the coefficients of the variables in the first three columns and the constants in the last column.

The augmented matrix will look like this:

\[ \begin{bmatrix} 3 & 1 & 4 & | & 9 \ 2 & -6 & -1 & | & 4 \ 1 & -7 & -6 & | & -9 \end{bmatrix} \]

However, we typically write the augmented matrix without the vertical line. Thus, the final augmented matrix is:

\[ \begin{bmatrix} 3 & 1 & 4 & 9 \ 2 & -6 & -1 & 4 \ 1 & -7 & -6 & -9 \end{bmatrix} \]