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3 and 4 .Determinants and Matrices
normal
The value of $a$ for which the system of equations
$a^3x + ( a + 1)^3y + (a + 2)^3z = 0$ ; $ax + (a + 1) y + ( a + 2) z = 0$ ; $x + y + z = 0$, has a non zero solution is
A
$1$
B
$0$
C
$-1$
D
none of these
Solution
The system of linear equation will have a non zero solution if
$\left|\begin{array}{ccc}a^{3} & (a+1)^{3} & (a+2)^{3} \\ a & (a+1) & (a+2) \\ 1 & 1 & 1\end{array}\right|=0$
Now operate $c_{2}-c_{1}$ and $c_{3}-c_{2},$ then expand.
Standard 12
Mathematics