Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 2 / 19D / c / i

First rotate rows $2,3$ with $c=4/5$, $s=3/5$. The second column pair $(4,3)$ becomes $(5,0)$ and the corresponding third column pair $(1,2)$ becomes $(2,1)$. Next rotate rows $3,4$ with $c=4/5$, $s=3/5$, sending the third column pair $(1,3/4)$ to $(5/4,0)$. Thus $R=G_{34}{G}_{23}A$ and $Q=G_{23}^T{G}_{34}^T$. One exact QR decomposition isThe construction proves $Q^{T}Q=I$, and direct multiplication checks $QR=A$.