DeterminantHard

Question

The value of a for which system of equations, a3x + (a + 1)3y + (a + 2)3z = 0,
ax + (a + 1) y + (a + 2) z = 0, x + y + z = 0, has a non-zero solution is:

Options

A.-1
B.0
C.1
D.none of these

Solution

=  0 for non - zero solution
C2 → C2 - C1, C3 → C3 - C1
= 0
⇒  2((a + 1)3 - a3) - ((a + 2)3 - a3) = 0   ⇒   2 (3a2 + 3a + 1) = 6a2 + 12a + 8
⇒  6a + 2 = 12 a + 8   ⇒ -  6 = 6a
⇒  a = - 1

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