## anonymous 5 years ago let v=(1,9,-1,5). find a basis of the subspace of R^4 of all vectors perpendicular to v.

Perpendicular to v$\rightarrow x_1 + 9x_2 -x_3 + x_4 = 0 \rightarrow x_3 = x_1 + 9x_2 + x_4$ Then by decomposition we have $\rightarrow \{<1,0,1,0>, <0,1,9,0>, <0,0,1,1>\}$ is a basis of the subspace.