Algebra bases

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

Determine the coordinates of vector in the basis of

Indice

Solve the system inferred from the equaltiy

Solution

We look for two real numbers and such that: which is equivalent to:

The first equation gives us and by reporting this in the second one, we have: which implies then

The coordinates of vector in basis of are therefore

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