`|[xp+y, x, y] , [yp+z, y, z] , [0, xp+y, yp+z]|=0` if

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

Select and write the correct answer from the given alternatives in each of the following:The determinant |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 for all p in R if

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

Find the values of x, y, z , if the matrix A=[[0, 2 y, z],[ x, y, -z],[ x, -y, z]] satisfy the equation A^' A=I

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

Find the values of x, y, z if the matrix A=[[0, 2y, z],[ x, y,-z],[ x,-y, z]] satisfy the equation A^(prime)A=I .

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

If [[x-y-z] , [-y+z] , [z]] = [[0], [5] , [3]] then find the values of x, y and z

Solve the system: x + y - 2z = 0, 2x - 3y + z = 0, 3x - 7y + 10z = 0, 6x - 9y + 10z = 0.