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The system of equations 

2x + 2y – 3z = 1, 

4x + 4y + z = 2, 

6x + 6y – z = 3 has 

  • a)
    No solution 

  • b)
    Two solutions

  • c)
    Infinite many solution 

  • d)
    A unique solution 

Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The system of equations2x + 2y – 3z = 1,4x + 4y + z = 2,6x + 6y ...
The matrix form of the system of equation is AX = b

The augmented matrix is

Applying R2 → R2 - 2R1 , R3  → R3 - 3R1, we have


Apply R3 → R3 - 8R2

Hence, the rank of the matrix is equal to 2 i.e. r ( A | b) = 2.
Here, rank(A) = 2 = rank[A|b] < no of unknowns = 3. So there are infinite many solution of the system of equations.
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Most Upvoted Answer
The system of equations2x + 2y – 3z = 1,4x + 4y + z = 2,6x + 6y ...
The system of equations is incomplete. Please provide the remaining equations.
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The system of equations2x + 2y – 3z = 1,4x + 4y + z = 2,6x + 6y – z = 3 hasa)No solutionb)Two solutionsc)Infinite many solutiond)A unique solutionCorrect answer is option 'C'. Can you explain this answer?
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