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:
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 solutionC2 → 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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