[0,x-y,x-z],[y-x,0,y-z],[z-x,z-y,0]|=......

|{:(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0):}|=".........."

|(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)| is equal to……………

|(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)| is equal to……………

Without expanding show that : |(x-y,y-z,z-x),(y-z,z-x,x-y),(z-x,x-y,y-z)|=0

If Delta= [[0 , x , -y ],[-x , 0 , z],[ y , -z , 0 ]] then

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .

|{:(" "0," "x,y),(-x," "0,z),(-y,-z,0):}|=0

Matrix A=[{:(0,2y,z),(x,y,-z),(x,-y,z):}] if A A^(T)=I then , (x,y,z)=(...,...,...)(x,y,zgt0)

The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0 if (a) x y z are in AP (b) x y z are in GP (c) x y z are in HP (d) xy yz zx are in AP