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General
Easy

Question

If the matrix A = open square brackets table row 8 cell – 6 end cell 2 row cell – 6 end cell 7 cell – 4 end cell row 2 cell – 4 end cell lambda end table close square brackets is singular, then λ equal to -

  1. – 5    
  2. 1    
  3. 3    
  4. –1    

The correct answer is: 3


    A = Singular rightwards double arrow|A| = 0
    open vertical bar table row 8 cell – 6 end cell 2 row cell – 6 end cell 7 cell – 4 end cell row 2 cell – 4 end cell lambda end table close vertical bar = 0
    rightwards double arrow8(7λ – 16) + 6(– 6λ + 8) + 2(24 – 14) = 0
    rightwards double arrow 56λ –128 –36λ + 48 + 20 = 0
    rightwards double arrow 20λ = 60 rightwards double arrow λ = 3

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