Discussion Forum



1)

Let AX=D be a system of three  linear  non-homogeneous equations, If |A|  =0 and rank(A) =rank ([AD])= $\alpha$  , then 


A) AX=D will have infinite number of solutions when $\alpha$=3

B) AX=D will have unique solution when $\alpha$ <3

C) AX=D will have infinite number of solutions when $\alpha$ < 3

D) AX=D will have no solution when $\alpha$ <3

Answer:

Option C

Explanation:

 Given,

AX=D  be a system of three linear non-homogeneous equation. 

|A|=0

$\therefore$  Equation have not unique solution

But rank (A) = rank (AD) = $\alpha$

$\therefore$  If $\alpha$ < 3, then equation has infinite number of solutions