#### need solution for rd sharma maths class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 7

$x=y=z=0$

Hint:

If $\left | A \right |\neq 0$, then $x=y=z=0$

Given:

$3x+y-2z=0$

$x+y+z=0$

$x-2y+z=0$

Explanation:

The given homogeneous system can be written in matrix form

i.e.    $\begin{bmatrix} 3 & 1 &-2 \\ 1& 1 &1 \\ 1& -2 &1 \end{bmatrix}\begin{bmatrix} x\\ y\\ z\end{bmatrix} = \begin{bmatrix} 0\\ 0\\ 0\end{bmatrix}$

$A= \begin{bmatrix} 3 & 1 &-2 \\ 1& 1& 1\\ 1& -2 & 1 \end{bmatrix}$

Let

$\left | A \right |= \begin{vmatrix} 3& 1 &-2 \\ 1& 1& 1\\ 1& -2 & 1 \end{vmatrix}$

$=3(1+2)-1(1-1)-2(-2-1)$

$=9+0+6$

$=15$

$\left | A \right |\neq 0$

Hence, $x=0, y=0, z=0$