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LCSphysicist
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W = {f(t) | f(0) = 2f(1)}
The answer say yes, but i don't know how to prove the neutral element.
The answer say yes, but i don't know how to prove the neutral element.
What would be the zero?LCSphysicist said:W = {f(t) | f(0) = 2f(1)}
The answer say yes, but i don't know how to prove the neutral element.
i have no idea :|, the answer is literally "yes", just it.fresh_42 said:What would be the zero?
What does ##f(t)## stand for? A certain number at a point ##t##, or what does it mean?LCSphysicist said:i have no idea :|, the answer is literally "yes", just it.
fresh_42 said:What does ##f(t)## stand for? A certain number at a point ##t##, or what does it mean?
I know. I just want to get the OP think about it. The question is trivial once it is understood, so it is all about understanding, not answering.Math_QED said:My guess is that it is the usual abuse of notation.
In order to prove this property, you only have to show that zero is in that space. Now what is zero in this context?LCSphysicist said:Oh i forgot, subspace of the P(R) space of the real polynomials. You know:
The conjunt of reals Polynomials n deegre or smaller more the nule polynomial.
Yes, indeed is a trivial question, actually it's in a book introductory to linear algebra, but i still don't understand how to prove this item.
What's a conjunt? What does nule mean? I'm trying to figure out what that sentence was intended to mean.LCSphysicist said:The conjunt of reals Polynomials n deegre or smaller more the nule polynomial.
I assume the OP may be a native Spanish spraker. "Conjunto" is Spanish for "Set" and "Nulo" is Spanish for null. And for others, I assume, per abuse of notation, f(t) is a function. I assume the 0 vector here would be the 0 function/polynomial.vela said:What's a conjunt? What does nule mean? I'm trying to figure out what that sentence was intended to mean.
LCSphysicist said:W = {f(t) | f(0) = 2f(1)}
The answer say yes, but i don't know how to prove the neutral element.
Eclair_de_XII said:Question: Would the nature of the answer change if the superspace of ##W## were instead just the space of continuous functions, or maybe just another vector space consisting of real-valued functions defined at ##x=0## and ##x=1##?
WWGD said:I assume the OP may be a native Spanish spraker. "Conjunto" is Spanish for "Set" and "Nulo" is Spanish for null. And for others, I assume, per abuse of notation, f(t) is a function. I assume the 0 vector here would be the 0 function/polynomial.
Yes. I also speak Spanish and this is true.WWGD said:I assume the OP may be a native Spanish spraker. "Conjunto" is Spanish for "Set" and "Nulo" is Spanish for null. And for others, I assume, per abuse of notation, f(t) is a function. I assume the 0 vector here would be the 0 function/polynomial.
But read above where he said he's Brazilian.MidgetDwarf said:Yes. I also speak Spanish and this is true.
Spanish and Portuguese share a lot of words. Brazilian Portuguese is a dialect of Portuguese.WWGD said:But read above where he said he's Brazilian.
A linear subspace is a subset of a vector space that satisfies two conditions: closure under vector addition and closure under scalar multiplication. This means that any linear combination of vectors in the subspace will also be in the subspace.
To determine if something is a linear subspace, you must check if it satisfies the two conditions of closure under vector addition and scalar multiplication. You can also check if it contains the zero vector and if it is closed under taking linear combinations.
Yes, a linear subspace can contain only one vector. This vector would be considered the zero vector, as it is closed under scalar multiplication and vector addition.
Yes, the intersection of two linear subspaces is always a linear subspace. This is because it satisfies the two conditions of closure under vector addition and scalar multiplication.
Yes, a linear subspace can be infinite. For example, the set of all polynomials of degree 2 or less is an infinite linear subspace.