Q. 4.73 - Intermediate Algebra

Question

Write each system of linear equations as an augmented matrix: 

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

Step-by-Step Solution

Answer

Augmented matrix of given system of linear equations :

Part $\left(a\right) \left[\begin{array}{rrr}3& 8& -3\\ 2& 5& -3\end{array}\right]$

Part $\left(b\right) \left[\begin{array}{rrrr}2& -5& 3& 8\\ 3& -1& 4& 7\\ 1& 3& 2& -3\end{array}\right]$

Part (a) Step 1. Given Information

Given system of linear equations is :-

$\left(a\right)\left\{\begin{array}{l}3x+8y=-3\\ 2x=-5y-3\end{array}\right.$

Part (a) Step 2. Write the equations in Standard form.

The second equation is not in standard form. 

We rewrite the second equation in standard form.

$2x=-5y-3$

$2x+5y=-3$

Part (a) Step 3. Write Augmented matrix.

We replace the second equation with its standard form. 

In the augmented matrix, the first equation gives us the first row and the second equation gives us the second row. 

The vertical line replaces the equal signs.

$\left\{\begin{array}{l}3x+8y=-3 \\ 2x+5y=-3\end{array}\right. \left[\begin{array}{rrr}3& 8& -3\\ 2& 5& -3\end{array}\right]$

Part (b) Step 1. Given Information.

Given system of linear equations is :-

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

Part (b) Step 2. Write the equations in Standard form.

All three equations are in standard form.

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

Part (b) Step 3. Write Augmented matrix.

In the augmented matrix the first equation gives us the first row, the second equation gives us the second row, and the third equation gives us the third row. 

The vertical line replaces the equal signs.

 $\left\{\begin{array}{l}2x-5y+3z=8\\ 3x-y+4z=7\\ x+3y+2z=-3\end{array}\right. \left[\begin{array}{rrrr}2& -5& 3& 8\\ 3& -1& 4& 7\\ 1& 3& 2& -3\end{array}\right]$