Question

Find the values of x, y, z respectively if the matrix A `= [(0,2"y","z"),("x","y","-z"),("x","-y","z")]` satisfy the equation A^TA = I₃.

Options

• `1/sqrt2, 1/sqrt6, 1/sqrt3`

• `(-1)/sqrt2, (-1)/sqrt6, (-1)/sqrt3`

• Both `1/sqrt2, 1/sqrt6, 1/sqrt3` and `(-1)/sqrt2, (-1)/sqrt6, (-1)/sqrt3`

•  None of these

Answer 1

Both `1/sqrt2, 1/sqrt6, 1/sqrt3` and `(-1)/sqrt2, (-1)/sqrt6, (-1)/sqrt3`