Question

Write each system of linear equations as an augmented matrix:

Part (a): $\left\{\begin{array}{l}3x-y=-4\\ 2x=y+2\end{array}\right.$

Part (b):$\left\{\begin{array}{l}x-3y-4z=-2\\ 4x+2y+2z=5\\ 2x-5y+7z=-8\end{array}\right.$

Short answer

Part (a): The augmented matrix is $\left[\begin{array}{rrr}3& -1& -4\\ 2& -1& 2\end{array}\right]$.

Part (b): The augmented matrix is $\left[\begin{array}{cccr}1& -3& -4& -2\\ 4& 2& 2& 5\\ 2& -5& 7& -8\end{array}\right]$.

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given system of equations,

$\left\{\begin{array}{l}3x-y=-4\\ 2x=y+2\end{array}\right.$

Here, the second equation is not in standard form.

Rewrite the second equation in standard form,

$$\begin{gathered} 2x=y+2 \\ 2x-y=2 \end{gathered}$$

Part (a) Step 2. Write in augmented matrix.

Write the standard form of the second equation,

$\left\{\begin{array}{l}3x-y=-4\\ 2x-y=2\end{array}\right.$

Write the augmented matrix,

$\left[\begin{array}{rrr}3& -1& -4\\ 2& -1& 2\end{array}\right]$

Part (b) Step 1. Given information.

Consider the given system of equations,

$\left\{\begin{array}{l}x-3y-4z=-2\\ 4x+2y+2z=5\\ 2x-5y+7z=-8\end{array}\right.$

Here all the equations are in the standard form.

Write the augmented matrix,

$\left[\begin{array}{cccr}1& -3& -4& -2\\ 4& 2& 2& 5\\ 2& -5& 7& -8\end{array}\right]$