# 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

Write out the system of equations that corresponds to each of the following augmented matrices:
(a)$\left(\begin{array}{cccc}3& 2& |& 8\\ 1& 5& |& 7\end{array}\right)$
(b)$\left(\begin{array}{ccccc}5& -2& 1& |& 3\\ 2& 3& -4& |& 0\end{array}\right)$
(c)$\left(\begin{array}{ccccc}2& 1& 4& |& -1\\ 4& -2& 3& |& 4\\ 5& 2& 6& |& -1\end{array}\right)$
(d)$\left(\begin{array}{cccccc}4& -3& 1& 2& |& 4\\ 3& 1& -5& 6& |& 5\\ 1& 1& 2& 4& |& 8\\ 5& 1& 3& -2& |& 7\end{array}\right)$
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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
Hence, the system of equation of the given augmented matrix is $\left\{\begin{array}{l}3{x}_{1}+2{x}_{2}=8\\ {x}_{1}+5{x}_{2}=7\end{array}$
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
Hence, the system of equation of the given augmented matrix is $\left\{\begin{array}{l}5{x}_{1}-2{x}_{2}+{x}_{3}=3\\ 2{x}_{1}+3{x}_{2}-4{x}_{3}=0\end{array}$
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
Hence, the system of equation of the given augmented matrix is $\left\{\begin{array}{l}2{x}_{1}+{x}_{2}+4{x}_{3}=-1\\ 4{x}_{1}-2{x}_{2}+3{x}_{3}=4\\ 5{x}_{1}+2{x}_{2}+6{x}_{3}=-1\end{array}$
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
Hence, the system of equation of the given augmented matrix is $\left\{\begin{array}{l}4{x}_{1}-3{x}_{2}+{x}_{3}+2{x}_{4}=4\\ 3{x}_{1}+{x}_{2}-5{x}_{3}+6{x}_{4}=5\\ {x}_{1}+{x}_{2}+2{x}_{3}+4{x}_{4}=8\\ 5{x}_{1}+{x}_{2}+3{x}_{3}-2{x}_{4}=7\end{array}$

Jeffrey Jordon