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Let v,u,w be linearly dependent vectors in a vector space over R.

u1 = 2u

v1 = -3u+4v

w1 = u+2v-aw (a scalar from R)

(1) the vectors u1, v1 and w1 are linearly dependent for every value of a

(2) the vectors u1, v1 and w1 are linearly independent for every value of a

(3) the vectors u1, v1 and w1 are linearly independent for every value of a apart from 0

(4) the vectors u1, v1 and w1 are linearly independent for every positive value of a

(5) there exists a value of a for which the vectors u1, v1 and w1 are linearly independent

Thanks a lot !!