3. (10%) Let \( \mathbf{S} \) be the two-dimensional subspace of \( \mathbf{R}^3 \) spanned by \( \mathbf{x}1 = [1, 0, 2]^{\mathrm{T}} \) and \( \mathbf{x}2 = [0, 1, -4]^{\mathrm{T}} \). Find a basis for \( \mathbf{S}^\perp \).