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Consider the system of equations : x+a y=0, y+a z=0 and z+a x=0 . Then the set of all real values of ' a ' for which the system has a unique solution is:

Options

  1. AR - 1
  2. BR - -1
  3. C1,-1
  4. D1,0,-1

Correct answer

B. R - -1

Step-by-step solution

Given system of equations is homogeneous which is aligned &x+a y=0 &y+a z=0 &z+a x=0 aligned It can be written in matrix form as A = ( array lll 1 & a & 0 0 & 1 & a a & 0 & 1 array ) Now, | A |= [1-a (-a^2 ) ]=1+a^3 0 So, system has only trivial solution. Now, | A |=0 only when a=-1 So, system of equations has infinitely many solutions which is not possible because it is given that system has a unique solution. Hence set of all real values of ' a ' is R - -1

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