Hello, angelme!
We want nonzero numbers so that:
. .
. .
. .
Two polynomials are equal if their corresponding coefficients are equal:
. . . .
Solve the system: .
Show that {x^{2} , x^{2}+x+1, x^{2}+x, x-1} is LD
I took like 20 mins to find the solution with trial and error to get
(x^{2}+x) - 1/2(x^{2}+x+1) -1/2(x-1) -1/2(x^{2}) =0 ---> LD
Are there any formula or shortcut for this?
How about {x^{4}+x^{2}+1, x^{4}-x^{2}+1, x^{4}-x^{2}-1}?
Thank you Soraban!!!
So...for {x^{4}+x^{2}+1, x^{4}-x^{2}+1, x^{4}-x^{2}-1}
a(x^{4}+x^{2}+1) + b(x^{4}-x^{2}+1) + c(x^{4}-x^{2}-1) =0
(a+b+c)x^{4 }+ (a-b-c)x^{2 }+ (a+b-c) = 0
then I get
a=0
b=0
c=0
Does it mean it is LI?