Gram-Schmidt orthogonality

Question

Given a vector $v = (1,2,−1)$ in $\mathbb{R}^3$. Use the Gram-Schmidt process to find two vectors $v_1$ and $v_2$ such that $\{v,v_1,v_2\}$ is an orthogonal basis of $\mathbb{R}^3$.

Answer 1

HINT

Start with the basis

• $v=(1,2,-1)$
• $v_1=(1,0,1)$
• $u_2=(0,1,0)$

and apply the algorithm to obtain an orthogonal basis.

See also the related

• Gram Schmidt-The arts behind it
• Find orthonormal vectors for given vectors using Gram-Schmidt
• Is there a more convenient method for converting a base to be orthogonal than Gram Schmidt?