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` .

Find the values of x ,\ \ y\ ,\ z if the matrix A=[0 2y z x y-z x-y z] satisfy the equation A^T\ A=I_3 .

Find the values of x,y,z if the matrix A=[[0,2y,z],[x,y,-z],[x,-y,z]] satisfy the equation A^T A=I_3

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 .

If matrix A=[02 y z x y-zx-yz] satisfies AT = A-1, then find the value of x, y, z.

If matrix A=[(0, 2,y),( z, x, y),(-z, x-y, z)] satisfies A^T=A^(-1) , find x ,\ y ,\ zdot

Find the number of triplets (x, y, z) of integers satisfying the equations x + y = 1 - z and x^(3) + y^(3) =1-z^(2) (where z ne 1 )

Find the value of 4x^2+y^2+25 z^2+4x y-10 y z-20 z x when x=4,y=3 and z=2.

ii) Find the value of x,y,z where [[x+y,y-z],[1,7+x]] = [[4-x,z-4],[z-y,x+z+4]]

Find the value of 4x^2+y^2+25 z^2+4x y-10 y z-20 z x when x=4,\ y=3 and z=2

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