Matrices and Determinants 4 Question 20

21. 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

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Answer:

Correct Answer: 21. (a)

Solution:

  1. Given equations $x+a y=0, a z+y=0, a x+z=0$ has infinite solutions.

$ \begin{vmatrix} & 1 & a & 0 \\ & 0 & 1 & a & \\ & a & 0 & 1 \end{vmatrix} $=0

$\Rightarrow 1 +a^3 = 0$ or $a=-1$



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