Q46 / 160 · TS EAMCET 2019 (03 May Shift 1) · Mathematics

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

  • A
    $A X=D$ will have infinite number of solutions when $\alpha=3$
  • B
    $A X=D$ will have unique solution when $\alpha < 3$
  • Correct answer
    C
    $A X=D$ will have infinite number of solutions when $\alpha < 3$
  • D
    $A X=D$ will have no solution when $\alpha < 3$

Solution

Given, $A X=D$ be a system of three linear non-homogeneous equation. $|A|=0$ $\therefore$ Equation have not unique solution. But rank $(A)=\operatorname{rank}(A D)=\alpha$ $\therefore$ If $\alpha < 3$, then equation has infinite number of solutions.

Hence, the correct answer is option: 'C'.

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