- #1
Tala.S
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Hello everybody
I have to show that this set of vectors a = (e-t, e-it, et, eit ) is linearly independent.
My attempt :
f(x) = k1 * e-t + k2 * e-it + k3 * et + k4 * eit
f '(x) = k1 * -e-t + k2 * -ie-it + k3 * et + k4 * ieit
f ''(x) = k1 * e-t + k2 * -e-it + k3 * et + k4 * -eit
f(0) = k1 * 1 + k2 * 1 + k3 * 1+ k4 * 1 = 0
f '(0) = k1 * -1 + k2 * -i + k3 * 1+ k4 * i = 0
f ''(0) = k1 * 1 + k2 * -1 + k3 * 1+ k4 * -1 = 0
But when I plot this in maple and reduce it I get this :
- Image -
They're linearly dependent but this can't be correct. So I guess I'm doing something wrong but what ?
I would really appreciate it if someone could help me.
I HAVE SOLVED THIS !
I have to show that this set of vectors a = (e-t, e-it, et, eit ) is linearly independent.
My attempt :
f(x) = k1 * e-t + k2 * e-it + k3 * et + k4 * eit
f '(x) = k1 * -e-t + k2 * -ie-it + k3 * et + k4 * ieit
f ''(x) = k1 * e-t + k2 * -e-it + k3 * et + k4 * -eit
f(0) = k1 * 1 + k2 * 1 + k3 * 1+ k4 * 1 = 0
f '(0) = k1 * -1 + k2 * -i + k3 * 1+ k4 * i = 0
f ''(0) = k1 * 1 + k2 * -1 + k3 * 1+ k4 * -1 = 0
But when I plot this in maple and reduce it I get this :
- Image -
They're linearly dependent but this can't be correct. So I guess I'm doing something wrong but what ?
I would really appreciate it if someone could help me.
I HAVE SOLVED THIS !
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