Question

Is {[a b c] : a + 2b + c = 27} a subspace? I know what a subspace needs, but I have no idea what this even means. Thanks!

Answer 1

I guess the question is asking if the set of all a,b, and c such that
a+2b+c=27 is a subspace or not
new one on me :P

Answer 2

...a subspace of \(\mathbb R^3\) I assume

Answer 3

doesn't seem to be closed under scalar multiplication at least, right?
\(k(27)\neq27\) if \(k\neq1\)

Answer 4

not closed under addition either, so not a subspace

Answer 5

Thanks! Can you please explain what you did with k(27)?

Answer 6

let\[\vec u=a+2b+c=27\] and let \(k\) be some constant besides 0 or 1
well, if this is closed under scalar multiplication then\[\vec v=k\vec u=ka+2kb+kc=x+2y+z=k27\]if \(k=2\) for example we have\[\vec v=x+2y+z=54\]which is not in the space specified

Answer 7

...because the space must include vectors only of the form\[a+2b+c=27\]and this is not of that form
(the letters of the variables are, of course, unimportant)

Answer 8

I get it thanks!

Answer 9

welcome :)