Determine whether the following are subspaces of C[-1,1]:
(c) The set of continous nondecreasing functions on [-1,1]
I already know how to prove that something is a subspace, but the problem here is in the term nondecreasing which i don't know how to turn it into a "such that" statement to test it
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Try: A function \(f(x)\) is non-decreasing on an interval \(I\) if \(f(a)\leq f(b)\) for all \(a, b \in I\) such that \(a < b\).
i'm not sure if you can see what I wrote, i'm not good with the equation typing buton
Not the answer you are looking for? Search for more explanations.
What was cut off at the end? I can only read "\(\alpha f(x)\) might be decre...."
By the way, if you want put \(\LaTeX\) in line, type "\.( the stuff you want the be in math format \.)" Just remove the periods.
"\ ( if i want to test for closure under scalar multiplication, i will do the following
if f in C[-1,1] then alpha f in C[-1,1] also f(x) is non-decreasing means that
alpha f(x) might be decreasing when alpha is negative or so ? \)"
this would mean that f is not in c[-1,1] ?
I believe so. Since it isn't closed under scalar multiplication, not a subspace.
hence my counter example above.
from your example, we can write the statement "is non-decreasing" as "f(x) = x is non decreasing" ?
Yes. Assume \(f(x)\) is non-decreasing, then \((-1)f(x)\) is decreasing.