Question

Write each system of linear equations as an augmented matrix:

Part (a):$\left\{\begin{array}{l}2x-5y=-3\\ 4x=3y-1\end{array}\right.$

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

Short answer

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

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

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given system of equations,

$\left\{\begin{array}{l}2x-5y=-3\\ 4x=3y-1\end{array}\right.$

Here, the second equation is not in standard form.

Rewrite the second equation in standard form,

$$\begin{gathered} 4x=3y-1 \\ 4x-3y=-1 \end{gathered}$$

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

Write the standard form of the second equation,

$\left\{\begin{array}{l}2x-5y=-3\\ 4x-3y=-1\end{array}\right.$

Write the augmented matrix,

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

Part (b) Step 1. Given information.

Consider the given system of equations,

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

Here all the equations are in the standard form.

Write the augmented matrix,

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