Answer to Question #327880 in Linear Algebra for Dudu

Question

1.Suppose A and B are both non zero real numbers.find real numbers C and D such that 1/a+ib=c+id.

2.suppose v,w€v.explain why there exists a unique x€v such that v+3x=w.

3.find all values of alpha€c such that alpha(1+I;2-i)=(2+2i;2-i).

4.let -infinity and positive infinity denote two distinct objects,neither of which is in R. Define an addition and scalar multiplication on RU{+infinity} U{-infinity}. specifically,the sum and product of two real numbers is as usual, and for T€R define

T(+infinity)=[-infinity if t<0

[0 if t=0

[+Infinity if t>o

T(-infinity)=[+infinity if t<0

[0 if t=o

[-infinity if t>0,

T+infinity=infinity+t=infinity,t+(-infinity)=-infinity+t=-infinity.

Infinity+infinity=infinity,(-infinity)+(-infinity)=-infinity, infinity+(-infinity)=o

Determine whether RU(infinity)U (-infinity) is a vector space over R.