Question

Construct an augmented matrix for this linear system:

x − y − 4z = 5
2x + 2z = 0
4x + y + z = 3

Answer 1

in the pic

Explanation:

Answer 2

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

Explanation:

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (including 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`

Hence, an 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)`