Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Digital systems, linear algebra, introduction to formal proof / 4 / e / Solution

The Gram-Schmidt process first gives $u_1=a_1=(1,1,1,1{)}^T$, of norm two. Next $a_1^T{a}_2/(a_1^T{a}_1)=2$, soFor the third column, both coefficients onto $u_1,u_2$ equal one, givingThese three nonzero vectors are mutually orthogonal and each has norm two. The resulting orthonormal basis is