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` .

Answer

N/a

Explanation

`Here A=[{:(0,2y,z),(x,y,-z),(x,-y,z):}]`
` A'=[{:(0,x,x),(2y,y,-y),(z,-z,z):}]`
Given that ,
`A'A=I`
`implies[{:(0,x,x),(2y,y,-y),(z,-z,z):}][{:(0,2y,z),(x,y,-z),(x,-y,z):}]=I`
`implies [{:(0+x^(2)+x^(2),0+xy-xy,0-1xz+xz),(0+xy-xy,4y^(2)+y^(2)+y^(2),2yz-yz-yz),(0-xz+xz',2yz-yz-yz,z^(2)+z^(2)):}]=I`
`implies [{:(2x^(2),0,0),(0,6y^(2),0),(0,0,3z^(2)):}]=[{:(1,0,0),(0,1,0),(0,0,1):}]`
` implies 2x^(2) =1,6y^(2)=1,3z^(2) =1`
` implies x=+- (1)/(sqrt(2)),y=+-(1)/(sqrt(6)),z=+-(1)/(sqrt(3))`