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Question
Select the correct option from the given alternatives:
The value of a for which system of equation a3x + (a + 1)3 y + (a + 2)3z = 0 ax + (a +1)y + (a + 2)z = 0 and x + y + z = 0 has non zero Soln. is
Options
0
–1
1
2
Solution
–1
Explanation:
The given system of equations will have a non-zero solution, if
`|("a"^3, ("a" + 1)^3, ("a" + 2)^3),("a", "a" + 1, "a" + 2),(1, 1, 1)|` = 0
Applying C2 → C2 – C1, C3 → C3 – C2, we get
`|("a"^3, 3"a"^2 + 3"a" + 1, 3"a"^2 + 9"a" + 7),("a", 1, 1),(1, 0, 0)|` = 0
∴ a3(0 – 0) – (3a2 + 3a + 1) (0 – 1) + (3a2 + 9a + 7) (0 – 1) = 0
∴ –6a – 6 = 0,
∴ a = – 1
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