Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.1 Determine which of the following binary operations are associative. The operation $\star$ on $\mathbb{Z}$ defined by…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.7 Let $f : A \rightarrow B$ be a surjective map of sets. Prove that the relation…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.6 Determine whether the function $f : \mathbb{R}^+ \rightarrow \mathbb{Z}$ given by mapping a real number $r$…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.5 Determine whether the following functions are well defined. $f : \mathbb{Q} \rightarrow \mathbb{Z}$ given by $f(a/b)…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.4 Denote by $\mathcal{A}$ the set of all $2\times 2$ matrices with real number entries. Let $M…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.3 Denote by $\mathcal{A}$ the set of all $2\times 2$ matrices with real number entries. Let $M…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.2 Denote by $\mathcal{A}$ the set of all $2\times 2$ matrices with real number entries. Let $M…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 0.1 Exercise 0.1.1 Denote by $\mathcal{A}$ the set of all $2\times 2$ matrices with real number entries. Let $M…
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