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A system o f linear equations x + 2 y - z = l l , 3 x + y - 2 z = 10, x - 3y = 5 has
  • a)
    no solution
  • b)
    exactly one solution
  • c)
    exactly 3 solutions
  • d)
    infinitely many solution
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A system o f linear equations x + 2 y - z = l l , 3 x + y - 2 z = 10, ...
We are given that the system of equation
x + 2y - z =11
3 x + y - 2z = 10
x - 3 y = 5
The given system of equation can be written in the augmented matrix as,

Applying the operations "R2 ---> R2 - 3R1" and R3 —> R3 - Rthese operations yield

and also "R3 ---> R3 - R2 ", which gives,

Here, rank of (A) ≠ rank of aug (A).
Hence, the given system of equation has no solution.
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Most Upvoted Answer
A system o f linear equations x + 2 y - z = l l , 3 x + y - 2 z = 10, ...
We are given that the system of equation
x + 2y - z =11
3 x + y - 2z = 10
x - 3 y = 5
The given system of equation can be written in the augmented matrix as,

Applying the operations "R2 ---> R2 - 3R1" and R3 —> R3 - Rthese operations yield

and also "R3 ---> R3 - R2 ", which gives,

Here, rank of (A) ≠ rank of aug (A).
Hence, the given system of equation has no solution.
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A system o f linear equations x + 2 y - z = l l , 3 x + y - 2 z = 10, x - 3y = 5 hasa)no solutionb)exactly one solutionc)exactly 3 solutionsd)infinitely many solutionCorrect answer is option 'A'. Can you explain this answer?
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