Value of a for which system of equations a^3x + ( a + 1)^3y + (a + 2)^3z = 0 ; ax + (a + 1) y +

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3 and 4 .Determinants and Matrices

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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

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