Question

Which of the subsets of R^3 are actually subspaces?

Answer 1

\[U= \left\{ {\left(\begin{matrix}x \\ y\\z\end{matrix}\right) \epsilon \mathbb{R}^{3} : x=y } \right\}\]

Answer 2

How do I go about doing this? I don't have a good understanding on what to look for

Answer 3

I don't understand what the \[{\left(\begin{matrix}x \\ y\\z\end{matrix}\right) \epsilon \mathbb{R}^{3} : x=y }\] means

Answer 4

no sorry bbut do you know 7x-1<20

Answer 5

it means \[{\left(\begin{matrix}x \\ x\\z\end{matrix}\right) \epsilon \mathbb{R}^{3} : x=y }\]

Answer 6

what does the ER^3 mean

Answer 7

i means you are in the space \(\mathbb{R}^3\) i.e. vectors with three elements, all of which are real numbers

Answer 8

i.e. each vector has 3 elements, all of them are real numbers
just fancy language is all
but of course you could have vectors with complex numbers, or elements of some other field

Answer 9

So am I only trying to prove that the x=y satisfies the three conditions?

Answer 10

yes, and it should be really easy
they are just checking to see if you know the axioms for a vector subspace

Answer 11

is that clear? should take a second to show all 3 are true, if you know what you have to show

Answer 12

Kind of, I looked up examples online too and they changed the y to an x too. Why?

Answer 13

without meaning to sound like a wise guy, because if \(x=y\) then well... \(x=y\)

Answer 14

if \(x=y\) you can replace any \(y\) by \(x\)

Answer 15

OHHHH hahaha okay I get it now. Thank you!!

Answer 16

of course you could have written \[{\left(\begin{matrix}y\\ y\\z\end{matrix}\right) }\]

Answer 17

yw