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The system of linear equations in real (x, y) given by involves a real parameter 
a and has infinitely many non-trivial solutions for special value(s) of a . Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α ?
  • a)
    x = 2, y = -2
  • b)
    x = -1, y = 4
  • c)
    x = 1, y= 1
  • d)
    x = 4, y = -2
Correct answer is option 'A,B'. Can you explain this answer?
Most Upvoted Answer
The system of linear equations in real (x, y) given byinvolves a real ...
Given : The system of linear equations in real (x, y),

As we know that, System of linear equation,
AX = 0 …(ii)
By equation (i) and (ii), we get
Matrix 
It has infinity many non-trivial solutions for special values of a.
That means det (A) will be zero.

For α = 2,

System of linear equation will be,

2x + 2y= 0 and x + y= 0
x = -y …(iii)
For α = 1/2,

System of linear equation will be,

2x + y/2  = 0 and 4x +y=0
2x = -y/2
4x = -y ....(iv)
For equation (iii) and (iv), only x =-1, y = 4 and  x = 2, y =- 2 are satisfied.
Hence, the correct option are (A,B).
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The system of linear equations in real (x, y) given byinvolves a real parametera and has infinitely many non-trivial solutions for special value(s) of a . Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α ?a)x = 2, y = -2b)x = -1, y = 4c)x = 1, y= 1d)x = 4, y = -2Correct answer is option 'A,B'. Can you explain this answer?
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