Inner product/Kernel of 4 -3 2 -5/Orthonormal basis/Exercise

We endow ${}\mathbb {R} ^{4}$ with the standard inner product. Let ${}U\subseteq \mathbb {R} ^{4}$ be the kernel of the linear mapping

$\mathbb {R} ^{4}\longrightarrow \mathbb {R} ,(x,y,z,w)\longmapsto 4x-3y+2z-5w.$

Determine an orthonormal basis for ${}U$.

Create a solution