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 given linear equations will be constructed as follows

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

What will be the augmented matrix of the given linear equations?

The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.

The given equation has three variables so the matrix form will be of $3\times3$

The given linear equations are

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

From the above equations, we will make an augmented matrix.

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

The first equation will be followed by the first row of the matrix and the rest will be followed the same.

Thus the augmented matrix for the given linear equations will be constructed as follows

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

To learn more about the Augmented matrix follow

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Answer 2

The augmented matrix is,

$\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)$

We have given system of linear equation is,

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

What is the meaning of augmented matrix?

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.

So, the first row is

$1\ -1\ -4\ 5$

the second row is

$2\ 0\ 2\ 0$

and the third row is

$4\ 1\ 1\ 3$

Therefore the augmented matrix for this linear system is,

$\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)$

To learn more about the augmented matrix visit:

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