2024-12-26【Basic Abstract Algebra】Exercises for Section 3.5 — Fundamental Isomorphism theorem of groupLet\(G=\{(a,b)\mida,b\in\mathbbR,~a\neq0\}\)with\((a,b)(c,d)=(ac,ad+b)\)beagroup,\(K=\{(1,b)\midb\in\mathbbR\}\).Showthat\(G/K\cong\mathbbR^*\).Proof:Let\[\begin{aligned}\varphi:\quadG&\to\mathbbR^*\\