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For which value of the system of linear equation
3x – y + λz = 1,
2x + y + z = 2,
x + 2y – λz = –1 ?
have no sol.
Correct answer is '-3.5'. Can you explain this answer?
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Most Upvoted Answer
For which value of the system of linear equation3x – y + &lambda...
The matrix form of the given system of equations is
The given system of equations will have a unique solution if and only if the coefficient matrix is non-singular.
Performing R1 ↔ R3, we get
Therefore the coefficient matrix will be non-singular if and only if
i.e. 
Thus the given system will have a unique solution if λ ≠ -7/2
In case λ = -7/2 the equation (i) becomes
In case λ = -7/2 the equation (i) becomes
Performing R3 → R3 R2, we get
showing that given equations are inconsistent in this case.
Thus if λ = -7/2 = −3.5 , no solution exists.
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For which value of the system of linear equation3x – y + λz = 1,2x + y + z = 2,x + 2y – λz = –1 ?have no sol.Correct answer is '-3.5'. Can you explain this answer?
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