Answer to Question #282169 in Linear Algebra for JOY

Question #282169

Determine wheather the following sets are subspaces of R

3

{(a,b,c) : a

2+ b

2+ c

2 ≤1, a,b,c ∈R}


1
Expert's answer
2021-12-23T17:57:21-0500

Let us determine wheather the set W={(a,b,c):a2+b2+c21,a,b,cR}W=\{(a,b,c) : a^2+ b^2+ c^2 ≤1, a,b,c ∈\R\} is a subspace of R3.\R^3. Taking into account that 12+02+02=11,1^2+0^2+0^2=1\le1, we conclude that (1,0,0)W.(1,0,0)\in W. On the other hand, (1,0,0)+(1,0,0)=(2,0,0)W(1,0,0)+(1,0,0)=(2,0,0)\notin W because of 22+02+02=41.2^2+0^2+0^2=4\ge1. Therefore, WW is not a subspace of R3.\R^3.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment