I'm trying to complete the following exercise: Let V be the set of vectors (x_1,x_2,x_3,x_4) in RR^4 such that 2x_1−3x_2−x_3+x_4=0 x_1−x_2+2x_3−x_4=0 Show that V is a subspace of RR^4 and find a basis for V.

ajumbaretu 2022-11-20 Answered
I'm trying to complete the following exercise:
Let V be the set of vectors ( x 1 , x 2 , x 3 , x 4 ) R 4 such that
2 x 1 3 x 2 x 3 + x 4 = 0
x 1 x 2 + 2 x 3 x 4 = 0
Show that V is a subspace of R 4 and find a basis for V.
I already showed that V is a subspace of R 4 , but I'm having trouble finding a basis for V. Any help is welcome
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Answers (1)

Hector Hamilton
Answered 2022-11-21 Author has 13 answers
Actually, even more is true. For p > 0 and q > 0, we have that
lim x log p x x q = lim x ( log x x q / p ) p = ( lim x log x x q / p ) p = ( lim x 1 ( q / p ) x q / p ) p = 0
using continuity and l'Hôpital's rule.
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