Determine if the vectors v1 = (2, −1, 2, 3), v2 = (1, 2, 5, −1), v3 = (7, −1, 5, 8) are linearly independent vectors in r4 .

Vectors are linearly independent if there doesn't exist a non-trivial linear combination which returns the zero vector. So, we must see if we can find three coefficients such that

. We have

So,

This linear combination returns the zero vector if

This system admits the only trivial solution a=b=c=0, so the vectors are linearly independent.

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step-by-step explanation:

you put them as all the same denominator and multiply