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NDA2023MathematicsDeterminantsActual

Let A X=B be a system of 3 liner equations with 3 -unknowns. Let X₁ and X₂ be its two distinct solutions. If the combination a X₁+b X₂ is a solution of A X=B ; where a, b , are real numbers, then which one of the following is correct?

Options

  1. Aa=b
  2. Ba+b=1
  3. Ca+b=0
  4. Da-b=1

Correct answer

B. a+b=1

Step-by-step solution

A X=B A X₁=B and A X₂=B Since (a X_ + +b X₂ ) is also a solution. Hence, A (a X₁+b X₂ )=B a A X₁+b A X₂=Ba B+b B=BB(a+b)=B a+b=1

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