Oh, so when he says "Find a basis", he doesn't mean find all of the bases, he just means find a single vector in the basis?
So if I had another question "Find a basis for a subspace of R3 in which all vectors satisfy:
(1 1 0) v = 0
Then I could just give a vector like:
(-1, 1, 0)...
Hi, I had a basic linear algebra question
Question #1
Homework Statement
Find a basis for the subspace of R3 for which the components in all of the vectors sum to zero.
Homework Equations
If u and v are in w and w is a subspace, then a*u + b*v is in w.
The Attempt at a...
Okay, here's how I approached the problem.
u is in S \cap T
v is in S \cap T
a, b are scalars
If S \cap T is a subspace, then au + bv is in S \cap T.
If au + bv is in S \cap T, then au + bv is in both S and T.
au + bv is in S because S is a subspace and au + bv is in T because...
Thanks. Can I ask if I did another question correctly?
The question asks:
Show that if S and T are subspaces of a vector space V, then S \cap T is also a subspace.
My Solution thus far
S \cap T \subset S and S is a subspace, so S \cap T is also a subspace.
That almost...
The way I did it was:
W = {(f in C[0, 1]): f(1/2) = 0}
f(x) and g(x) are in the subset W
if W is a subspace then h(1/2) = 0 for h(x) = a*f(x) + b*g(x)
h(1/2) = a*f(1/2) + b*g(1/2)
h(1/2) = a*0 + b*0
h(1/2) = 0
So W is a subspace.
--
Does that seem about right?
I definitely understand the logic of what you're saying. If f(1/2) and g(1/2) are both 0, then (f + g)(1/2) will also be zero.
But I don't know how to say it formally.
Subspace of a Function?!?
Homework Statement
{f \in C([0, 1]): f(1/2) = 0}
Is this subset of C([0,1]) a subspace?
Homework Equations
C[0,1] be the set of all functions that are continuous on [0, 1].
(f + g)(x) = f(x) + g(x)
(af)(x) = a*f(x)
The Attempt at a Solution...
Yes, but I think my point still stands that it's hard for applicants to know how much being a star athlete, minority, or born into a low socioeconomic class matters in the admissions process - so we shouldn't be surprised that tons of kids apply to schools where they aren't competitive.
In...
Well, the actual problem I want to solve is:
F(s) = \int_{0}^{\infty} e^{-st}f(t) dt
for f(t). Now I want to take the derivative of both sides, and then multiply by e^{-st}, and then get f(t).
Now I know from looking at Laplace transforms that the infinity part always evaluates to...
How do I do it? For example, if I have:
\int_{0}^{\infty}sf(x) dx
How do I take the derivative with respect to x?
I was trying to derive the formula for an inverse laplace transform when I realized that I didn't know how to take the derivative of a definite integral.
Yes, but how do kids
For example, I got rejected at my first and third choices, and waitlisted at my second choice. For all 3 schools I was within the middle 50th percentiles for SATs and below average for grades. How was I supposed to know if my ECs would be good enough to overcome my grades?
But the situation sort of confuses applicants because these schools DO accept students with some SAT sections below 700, and it's hard for applicants to know if their "soft" factors compensate for below average test scores, since they don't know what admissions are like.
Hmmm... Joking aside, I'm curious if anyone has a correlation between physics grades and math grades? Or physics SAT subject test and Math SAT subject test.
He might be asking for a coefficient of correlation between mathematics ability and physics scores. That would tell him how much of being a successful physicist overlaps with mathematics.
Perhaps the collegeboard publishes a statistic like that?