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Q.
If $4x-ay+3z=0,x+2y+az=0$ and $ax+2z=0$ have a non-trivial solution, then the number of real value(s) of $a$ is
NTA AbhyasNTA Abhyas 2020Matrices
Solution:
For non-trivial solution, using Cramer's rule, we get,
$\begin{vmatrix} 4 & -a & 3 \\ 1 & 2 & a \\ a & 0 & 2 \end{vmatrix}=0$
$4\left(4 - 0\right)+a\left(2 - a^{2}\right)+3\left(0 - 2 a\right)=0$
$a^{3}+4a-16=0\Rightarrow \left(a - 2\right)\left(a^{2} + 2 a + 8\right)=0$
$a=2$
Hence, only one value of $a$