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If the system of equations :
x + 4ay + az = 0
x + 3by + bz = 0
x + 2cy + cz = 0
Has non trivial solution , then a, b , c one in
- a)A.P
- b)G.P
- c)H.P
- d)A.G.P
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the system of equations :x + 4ay + az = 0x + 3by + bz = 0x + 2cy + ...
∵ Given system of equation has non - trivial solutions , then
l A l = 0
On expanding , we get
- 2ac + ab + bc = 0
2ac = b ( a + c )
B = 2ac / a+c
Which is harmonic mean of a,b,c
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Community Answer
If the system of equations :x + 4ay + az = 0x + 3by + bz = 0x + 2cy + ...
Explanation:
Given System of Equations:
Equation 1: x + 4ay + az = 0
Equation 2: x + 3by + bz = 0
Equation 3: x + 2cy + cz = 0
Non-Trivial Solution:
To have a non-trivial solution, the determinant of the coefficients of x, y, and z in the system of equations must be zero.
Determinant Condition:
- For a non-trivial solution, the determinant of the coefficients must be zero.
- This means that the determinant of the matrix formed by the coefficients of x, y, and z must be zero.
Common Ratio for Non-Trivial Solution:
If the system of equations has a non-trivial solution, then the ratios of the coefficients a, b, and c must form a harmonic progression (H.P).
Conclusion:
Therefore, if the given system of equations has a non-trivial solution, the ratios of coefficients a, b, and c must be in a harmonic progression (H.P).
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If the system of equations :x + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz = 0Has non trivial solution , then a, b , c one ina)A.Pb)G.Pc)H.Pd)A.G.PCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If the system of equations :x + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz = 0Has non trivial solution , then a, b , c one ina)A.Pb)G.Pc)H.Pd)A.G.PCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the system of equations :x + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz = 0Has non trivial solution , then a, b , c one ina)A.Pb)G.Pc)H.Pd)A.G.PCorrect answer is option 'C'. Can you explain this answer?.
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