Construct an augmented matrix for this linear system:x βˆ’ y βˆ’ 4z = 52x + 2z = 04x + y + z = 3

Accepted Solution

Answer:[tex]\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)[/tex]Step-by-step 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 [tex]1\ -1\ -4\ 5[/tex]the second row is [tex]2\ 0\ 2\ 0[/tex]and the third row is [tex]4\ 1\ 1\ 3[/tex] Hence, an augmented matrix for this linear system is[tex]\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)[/tex]