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Determine all real numbers a for which the vectors v1 = (1,−1,1,a,2) v2 = (−1,0,0,1,0) v3...

Determine all real numbers a for which the vectors

v1 = (1,−1,1,a,2)
v2 = (−1,0,0,1,0)
v3 = (1,2,a + 1,1,0)
v4 = (2,0,a + 3,2a + 3,4)

make a linearly independent set. For which values of a does the set contain at least three linearly independent vectors?

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