- #1
csc2iffy
- 76
- 0
Homework Statement
This problem is broken into 5 parts:
(1) Let E={(2a,a)|a∈ℝ}. Is E a subspace of R2?
(2) Let B={(b,b)|b∈ℝ}. Is B a subspace of R2?
(3) What is E[itex]\cap[/itex]B?
(4) Is E[itex]\cup[/itex]B a subspace of R2?
(5) What is E+B
Homework Equations
E={(2a,a)|a∈ℝ}
B={(b,b)|b∈ℝ}
The Attempt at a Solution
(1) Yes, closed under addition and scalar mult.
(2) Yes, closed under addition and scalar mult.
(3) E[itex]\cap[/itex]B={(0,0)}
(4) E[itex]\cup[/itex]B={(2a,a),(b,b)|a,b[itex]\in[/itex]ℝ}
I don't know how to show if tis is a subspace of R2 or if that is the correct union
(5) i also do not know how to add them