Question

Write the augmented matrix for the following system of equations
0=-y+x
-x+2y=-2

Answer 1

To write the augmented matrix for the given system of equations, we first need to rearrange the equations in standard form (Ax + By = C).

The given equations are:

1. \( 0 = -y + x \) can be rewritten as \( x - y = 0 \) or \( x - y + 0 = 0 \).
2. \( -x + 2y = -2 \) can be rewritten as \( -x + 2y = -2 \).

Now, we can express this system in standard form:

1. \( x - y = 0 \)
2. \( -x + 2y = -2 \)

Next, we construct the augmented matrix. The coefficients of the variables \( x \) and \( y \) will form the left side of the matrix, and the constants on the right will form the augmented part.

The augmented matrix for this system is:

\[
\begin{bmatrix}
1 & -1 & | & 0 \\
-1 & 2 & | & -2
\end{bmatrix}
\]

This matrix represents the system of equations, with the vertical line separating the coefficients from the constants.