Question

Write each system of linear equations as an augmented matrix:

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

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

Short answer

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

Part (b): The augmented matrix is $\left[\begin{array}{cccr}3& -2& -1& -2\\ -2& 1& 0& 5\\ 5& 4& 1& -1\end{array}\right]$.

Step-by-step solution

Part (a) Step 1. Given information and write in augmented matrix.

Consider the given system of equations,

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

Here all the equations are in the standard form.

Write the augmented matrix,

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

Part (b) Step 1. Given information and write in augmented matrix.

Consider the given system of equations,

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

Here all the equations are in the standard form.

Write the augmented matrix,

$\left[\begin{array}{cccr}3& -2& -1& -2\\ -2& 1& 0& 5\\ 5& 4& 1& -1\end{array}\right]$