Question

What is the determinant of the coefficient matrix of the system –11 –2 0 55

Answer 1

The first two rows of coefficients are identical, so by inspection, the determinant is 0.

Answer 2

Answer:

The determinant of  coefficient  matrix of the given system is 0.

Step-by-step explanation:

Given system of equation

$-x-y-z=-3$

$-x-y-z=8$

$3x+2y+z=0$

The coefficient matrix of the system

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

Let A=$\left[\begin{array}{ccc}-1&-1&-1\\-1&-1&-1\\3&2&1\end{array}\right]$

X=$\left[\begin{array}{}x&y&z\end{array}\right]$

B=$\left[\begin{array}-3 &8&0\end{array}\right]$

Therefore , we can AX=B

$\left[\begin{array}{ccc}-1&-1&-1\\1&-1&-1\\3&2&1\end{array}\right]$$\left[\begin{array}{}x&y&z \end{array}\right]$=$\left[\begin{array}{}-3&8&0\end{array}\right]$

The determinant of  coefficient matrix of the given system is given by

$\begin{vmatrix}-1&-1&-1\\-1&-1&-1\\3&2&1\end{vmatrix}$

By using determinant property : when two rowsor two columns are identical then the value of determinant is equal to zero .

$\therefore \begin{vmatrix}A\end{vmatrix}=0$