Mathematics | TS EAMCET 2019 | Discussion Page

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

Option C

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

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