The discussion revolves around finding an annihilator for the expression x² + 2x⁵, which falls under the subject area of differential operators in the context of linear algebra or differential equations.
The discussion is active, with participants questioning assumptions about annihilators and exploring the relationships between different operators. Some guidance has been provided regarding the nature of annihilators, but no consensus has been reached on the best approach to take.
Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a focus on understanding the definitions and implications of the operators involved.
Doesn't the D6 operator also annihilate x2?magnesium12 said:Homework Statement
Find an annihilator of x2+2x5.
Homework Equations
xnecx -----> [D-c]n+1
[Q1(D)Q2(D)] = b1(x) + b2(x)
The Attempt at a Solution
[/B]
x2 -----> D3
2x5-----> D6
x2 + 2x5 ------> (D3)(D6) = D18
The answer should be D6.
Mark44 said:Doesn't the D6 operator also annihilate x2?
What does the last line mean? It's not clear to me.magnesium12 said:Homework Statement
Find an annihilator of x2+2x5.
Homework Equations
xnecx -----> [D-c]n+1
[Q1(D)Q2(D)] = b1(x) + b2(x)
Why are you multiplying the two annihilators?The Attempt at a Solution
[/B]
x2 -----> D3
2x5-----> D6
x2 + 2x5 ------> (D3)(D6) = D18
The answer should be D6.
Didn't notice this before -- is x3x6 = x18?magnesium12 said:(D3)(D6) = D18
Dn+1 annihilates xn and all lower powers of x. I don't see that this is related to the LCM in any way.magnesium12 said:I guess it does. So does that mean there can be multiple annihilators and they'll all work? Or should you always pick the least common multiple?
Heh...I didn't notice that either.Mark44 said:Didn't notice this before -- is x3x6 = x18?