Question

i will medal and fan

Answer 1

prove that the set M={(a,b,c,d)a,b,c,d \[inQ\]} with addition and multiplication define by
(a,b,c,d)+(e,f,g,h)=(a+e,b+f,c+g,d+h)
(a,b,c,d)(e,f,g,h)=(ae+bg,af+bh,ce+dg,cf+dh)
for all (a,b,c,d)(e,f,g,h) \[inm\] is a ring

Answer 2

\(M=\{(a,b,c,d)| a, b, c, d \in \mathbb Q\}\) defined by
\((a,b,c,d)+(e,f,g,h)=(a+e, b+f, c+g, d+h)\\(a,b,c,d)(e,f,g,h)=(ae+bg, af+bh, ce+dg, cf+dh)~~\forall a,b,c,d,e,f,g,h \in M\)
Prove that M is a ring

Answer 3

every element in M has the form (a,b,c,d). Imagine that a household with 4 members a, b, c, d where a is father, b is mother, c is son, d is daughter.
each group has all4 members like that is called the group of set M.

Answer 4

you need prove the axioms as what you did in previous question to prove M is a ring