Take 10 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
If you have more questions, feel to ask then on the forum.
Question
Prove that the familly of vectors of
is linearly independent.
Consider a linear combination
infer a system of equations and prove that it has
for only solution.
Let us consider a zero linear combination of the three vectors:
which is equivalent to:
which gives the system:
We infer from the first equation :
and by reporting into the last two equations, we have:-
The first equation gives
and by reporting in the second one, we obtain:
hence
which implies
then
The only zero linear combination of the three vectors is the one whose all coefficients are zero, therefore the family is linearly independent.
