The number of solutions of the following system of linear homogeneous equations x-y+z=0, x+2 y-z=0 and 2 x+y+3 z=0 is

Step-by-step solution

To find the number od solutions of the following system of linear homogeneous equations. aligned x-y+z & =0 ...(i) x+2 y-z & =0 ...(ii) 2 x+y+3 z & =0 ...(iii) aligned We can write the above equations in matrix form i.e. [ array ccc 1 & -1 & 1 1 & 2 & -1 2 & 1 & 3 array ] [ array l x y z array ]=0 or A X=0 , where A= [ array ccc 1 & -1 & 1 1 & 2 & -1 2 & 1 & 3 array ] Since, we know that, if |A|=0 , then only a non-trivial solution exist. Consider, |A|= [ array ccc 1 & -1 & 1 1 & 2 & -1 2 & 1 & 3 array ] aligned &