Homework Statement
f(x,y,z) = 4x^2 + y^2 + 9z^2
another one is xy+z^2
how do u draw level curves and graphs for these?
Homework Equations
The Attempt at a Solution
Just need somewhere to start
Thanks
that W is closed under addition and multiplication and it contains the zero vector.
But I don't understand how to show this, i mean like can't you just say f(y) + g(y) = 0 + 0 = 0 , where both f and g are in U?
criteria is that f(y) = 0
so let g(y) also be in U
f(y) + g(y) = (f+g)(y) = 0
for multiplication
c(f(y)) = (cf)(y) = 0
This is what I can come up with.
so is 0v just passes by the additive identity where f(y) + g(y) = 0 + 0 = 0?
can we just assume there is a non-zero vector a1, a2 that's in both m and n for it to be in m, we know a1 = x 1 and a2 = 0 component vector thingie and since it's a non-zero vector, you know x1 does not equal the zero component vector now, apply a1,a2 to N since a1 is not a zero-component...
So M and N intersect when (x,y) is contained in both M and N...
if M = (x1, 0v2) and N = (0v1, x2) shouldn't the intersection calculated by when the difference of those is = 0?
So you can get the point where both M and N contains?
Sorry about that typo.
So for the intersection, is when the two vectors intersect right? And this wants me to prove that their intersection is at the 0v. So can I do something like (x,y) - (a,b) = (0,0) <--(where x,y and a,b are two vectors, so the intersection is when they are at the same...