Matrices And Determinants Ques 95
If the system of equations $x+a y=0, a z+y=0$ and $a x+z=0$ has infinite solutions, then the value of $a$ is
(a) $-1$
(b) $1$
(c) $ 0$
(d) no real values
Show Answer
Answer:
Correct Answer: 95.(a)
Solution:
Formula:
System of equations with 3 variables:
- Given equations $x+a y=0, a z+y=0, a x+z=0$ has infinite solutions when $a = 1$ or $a = -1$.
$ \begin{vmatrix} & 1 & a & 0 \\ & 0 & 1 & a & \ & a & 0 & 1 \end{vmatrix} $=0
$\Rightarrow 1 +a^3 = 0$ or $a=-1$ is not correct. The equation $1 + a^3 = 0$ has a real solution $a = -1$, but it also has two complex solutions. Therefore, the statement is incomplete.
BETA
