Evaluate by using chio's method. `[(0,x,y,z),(-x,0,z,y),(-y,-z,0,x),(-z,-y,-x,0)]`

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

evaluate: |(a+x,y,z),(x,a+y,z),(x,y,a+z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

If x+y+z=pi then the value of |{:(sin(x+y+z),sin(x+z),cosy),(-siny,0,tanx),(cos(x+z),tan(y+z),0):}| is

Evaluate the following: |[0,x y^2,x z^2],[x^2y,0,y z^2],[x^2z, z y^2, 0]|

Find A=[(0,2y,z),(x,y,-z),(x,-y,z)] satisfies A^(T) = A^(-1)

Find the value of y, if the matrix A = ((0,2y,z),(x,y,-z),(x,-y,z)) obeys the law A^(T).A = I .

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2