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BITSAT2020MathematicsDeterminantsActual

Suppose p , q , r 0 and system of equation ( p + a ) x + by + cz =0a x+(q+b) y+c z=0a x+b y+(r+c) z=0 has a non-trivial solution, then value of a p + b q + c r is

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

A. -1

Step-by-step solution

Since the system is homogeneous and has a non-trivial solution 0= | array ccc p+a & b & c a & q+b & c a & b & r+c array |= | array ccc p & -q & 0 0 & q & -r a & b & r+c array | using R ₁ R ₁- R ₂ and R ₂ R ₂- R ₃ Expanding along C , we get p [ q ( r + c )+ br ]+ aqr =0 pqr + pqc + prb + qra =0 a p + b q + c r =-1

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