The determinant of the coefficient matrix of the system will be 0.
What is determinant?
The determinant in math is a scalar quantity that is a result of the rows and columns of a matrix form.
The system of the equations are given below.
–x – y + 2z = 5
3x + 2y – z = 3
4x + 4y – 8z = –2
Then the system of equation in the matrix form, we have
[tex]\begin{bmatrix}-1 & -1 & 2 \\3 & 2 & -1 \\4 & 4 & -8 \\\end{bmatrix}\begin{bmatrix}x \\y \\z \end{bmatrix} = \begin{bmatrix}5 \\ 3\\-2\end{bmatrix}[/tex]
Then the determinant of the coefficient matrix of the system will be
[tex]\begin{vmatrix}-1 & -1 & 2 \\3 & 2 & -1 \\4 & 4 & -8 \end{vmatrix}\\[/tex]
Take common 2, from third row.
[tex]2\begin{vmatrix}-1 & -1 & 2 \\3 & 2 & -1 \\1 & 1 & -2 \end{vmatrix}[/tex]
Add row 1 and 3 in row 1, we have
[tex]\begin{vmatrix}0 & 0 & 0 \\3 & 2 & -1 \\1 & 1 & -2 \end{vmatrix}\\[/tex]
The determinant of the coefficient matrix of the system will be 0.
More about the determinant link is given below.
https://brainly.com/question/13369636
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