TS EAMCET · Maths · Determinants
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 \(\alpha < 3\)
- C \(A X=D\) will have infinite number of solutions when \(\alpha < 3\)
- D \(A X=D\) will have no solution when \(\alpha < 3\)
Answer & Solution
Correct Answer
(C) \(A X=D\) will have infinite number of solutions when \(\alpha < 3\)
Step-by-step Solution
Detailed explanation
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.
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