question_answer

If a system of the equation \[{{(\alpha +1)}^{3}}x+{{(\alpha +2)}^{3}}y-{{(\alpha +3)}^{3}}z=0,\] \[(\alpha +1)x+(\alpha +2)y-(\alpha +3)z=0\]and\[x+y-z=0\]x + y - z = 0 has infinitely many solutions, then what is the value of a?

A) 1

B) 0

C) -3

D) -2

Correct Answer: D

Solution :

[d]: For infinitely many solutions, \[\left| A \right|=0\] i.e.. \[\Rightarrow \]\[6\alpha +12=0\Rightarrow \alpha =-2\].