The following is a linear algebra problem for inner product, length, and organality:
Let c={e1​,e2​,e3​,e4​} be the canonical basis of R⁴. Additionally, let b={u1​,u2​,u3​,u4​} be an orthogonal basis for R⁴ where u1​=[0,1,−4,−1], u2​=[3,5,1,1], u3​=[1,0,1,−4], and u4​=[5,−3,−1,1].
write each ei as a linear combination of the vectors in b using the dot product.