The augmented matrix for the linear system is constructed as
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right][/tex][tex]5\\0\\3\\[/tex]
The augmented matrix for the linear system of equation is used to represent equations in a matrix form and used to perform certain operations in the row of the given matrix.
The system of equation have 3 variables and we can represent it using a 3by3 matrix system.
The system of linear equation are
[tex]x-y-4z=5\\2x+2z=0\\4x+y+z=3[/tex]
With the equation above, we can proceed to construct the augmented matrix for this linear system
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right][/tex]=[tex]5\\0\\3\\[/tex]
The first equation is represented in the first horizontal row, the second and third equation are represented in the second and third rows respectively.
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