Question

Construct an augmented matrix for this linear system: x − y − 4z = 5 2x + 2z = 0 4x + y + z = 3.

Answer 1

The augmented matrix for the linear system is constructed as

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

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

$x-y-4z=5\\2x+2z=0\\4x+y+z=3$

With the equation above, we can proceed to construct the augmented matrix for this linear system

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

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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