(Lin Alg) is this Mapping between real vector spaces LINEAR or NON-LINEAR (please explain!!). L : R -- R defined as L(x) =2x+1

Thanks!

Question

(Lin Alg) is this Mapping between real vector spaces LINEAR or NON-LINEAR (please explain!!). L : R --> R defined as L(x) =2x+1

Thanks!

owlfred · Answer

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

anonymous · Answer

i think it is liear

anonymous · Answer

because for a definite x u find an unique L(x)

anonymous · Answer

A mapping between vector spaces is linear if:
1) L(x+y)=L(x)+L(y); where x and y are two vectors in the vector space
2) L(cx)= cL(c); c is a constant.

anonymous · Answer

Anwar A am i right?

anonymous · Answer

aNWAR THE GIVEN TWO CONDITIONS HOLDS HERE...

anonymous · Answer

thanks guys ya i kinda see it

anonymous · Answer

$L(x+y)=2(x+y)+1=2x+2y+1$. But $L(x)+L(y)=2x+1+2y+1=2x+2y+2$. Since $L(x+y)\ne L(x)+L(y)$. The mapping in NOT linear.

anonymous · Answer

@ dipankarstudy: The first condition is not hold.

anonymous · Answer

true lol

anonymous · Answer

yes.....thanks guys.

anonymous · Answer

how do i give medals or say good answer?

anonymous · Answer

Just click on "Good Answer" on the right upper corner of each comment.

anonymous · Answer

theres no such option on mine

anonymous · Answer

nvm i see it (im new to the site) thanks again!