Answer:
The determinant of coefficient matrix of the given system is 0.
Step-by-step explanation:
Given system of equation
[tex]-x-y-z=-3[/tex]
[tex]-x-y-z=8[/tex]
[tex]3x+2y+z=0[/tex]
The coefficient matrix of the system
[tex]\left[\begin{array}{ccc}-1&-1&-1\\-1&-1&-1\\3&2&1\end{array}\right][/tex]
Let A=[tex]\left[\begin{array}{ccc}-1&-1&-1\\-1&-1&-1\\3&2&1\end{array}\right][/tex]
X=[tex]\left[\begin{array}{}x&y&z\end{array}\right][/tex]
B=[tex]\left[\begin{array}-3 &8&0\end{array}\right][/tex]
Therefore , we can AX=B
[tex]\left[\begin{array}{ccc}-1&-1&-1\\1&-1&-1\\3&2&1\end{array}\right][/tex][tex]\left[\begin{array}{}x&y&z \end{array}\right][/tex]=[tex]\left[\begin{array}{}-3&8&0\end{array}\right][/tex]
The determinant of coefficient matrix of the given system is given by
[tex]\begin{vmatrix}-1&-1&-1\\-1&-1&-1\\3&2&1\end{vmatrix}[/tex]
By using determinant property : when two rowsor two columns are identical then the value of determinant is equal to zero .
[tex]\therefore \begin{vmatrix}A\end{vmatrix}=0[/tex]
