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 dependent.
Prove that the system of three equations with two unknow variables inferred from equality
has one solution.
We can try to prove that the second one is a linear combination of the others.
Since the result is not trivial, we set
which is equivalent to:
wiich gives:
The first equation gives
and the second one is satisfied by the pair
We therfore have:
which proves that the family is not linearly independent.
