Let

be the

matrix whose columns are

, and let

be the vector whose components are the constants

. Now consider the matrix equation

Multiplying both sides by

, we have

More explicitly, we're writing

Multiply both sides by

and the left hand side can be written as

We're told that

whenever

, so we're left with

Each of

are nonzero, which means their norms are nonzero, which necessarily implies that

, and so the vectors

must necessarily be linearly independent.
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P could equal +/- 1, +/- 2, +/- 11, +/-22
q could equal +/- 1, +/-2
so roots could be p/q = +/-1 , +/- 1/2 , +/- 2, +/- 11/2 , +/- 11, +/-22
That is the third choice.