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If a, b, c and vmatrix & b & c \ a & & c \ a & b & vmatrix = 0, then a - a + b - b + - c is equal to :
(4) 0
R1 R1 - R2, R2 R2 - R3:
vmatrix - a & b - & 0 \ 0 & - b & c - \ a & b & vmatrix = 0
Let p = - a, q = - b, r = - c (all 0); expand along R1:
p(q + br) + q(ar) = 0 pq + pbr + qar = 0
pqr 0, divide by pqr: r + bq + ap = 0
a - a + b - b + - c = 0
Answer: (4)
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