Write out the system of equations that corresponds to each of the following augmented matrices: (a)begin{pmatrix}3 & 2&|&8 1 & 5&|&7 end{pmatrix} (b)b

Step 1 Write out the system of equation to each of the following augmented matrices. Step 2 (a)$\left[\begin{array}{cccc}3& 2& |& 8\\ 1& 5& |& 7\end{array}\right]$
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $x_1\text{ and }{x}_2$
Hence, the system of equation of the given augmented matrix is $\{\begin{array}{l}3x_1+2x_2=8\\ x_1+5x_2=7\end{array}$
Step 3
(b)$\left[\begin{array}{ccccc}5& -2& 1& |& 3\\ 2& 3& -4& |& 0\end{array}\right]$
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $x_1,x_2\text{ and }{x}_3$
Hence, the system of equation of the given augmented matrix is $\{\begin{array}{l}5x_1-2x_2+x_3=3\\ 2x_1+3x_2-4x_3=0\end{array}$
Step 4
(c)$$\left[\begin{array}{ccccc}2& 1& 4& |& -1\\ 4& -2& 3& |& 4\\ 5& 2& 6& |& -1\end{array}\right]$$
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $x_1,x_2\text{ and }{x}_3$
Hence, the system of equation of the given augmented matrix is $\{\begin{array}{l}2x_1+x_2+4x_3=-1\\ 4x_1-2x_2+3x_3=4\\ 5x_1+2x_2+6x_3=-1\end{array}$
Step 5
(d)$\left[\begin{array}{cccccc}4& -3& 1& 2& |& 4\\ 3& 1& -5& 6& |& 5\\ 1& 1& 2& 4& |& 8\\ 5& 1& 3& -2& |& 7\end{array}\right]$
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $x_1,x_2,x_3\text{ and }{x}_4$
Hence, the system of equation of the given augmented matrix is $\{\begin{array}{l}4x_1-3x_2+x_3+2x_4=4\\ 3x_1+x_2-5x_3+6x_4=5\\ x_1+x_2+2x_3+4x_4=8\\ 5x_1+x_2+3x_3-2x_4=7\end{array}$

Answer is given below (on video)