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The system of linear equations
λx + 2y + 2z = 5
2λx + 3y + 5z = 8
4x + λy + 6z = 10 has
λx + 2y + 2z = 5
2λx + 3y + 5z = 8
4x + λy + 6z = 10 has
- a)infinitely many solutions when λ = 2
- b)no solution when λ = 8
- c)a unique solution when λ = -8
- d)no solution when λ = 2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The system of linear equationsλx + 2y + 2z = 52λx + 3y +...
⇒ Δx = 5(8) - 2(-2) + 2(-14)
Δx = 40 + 4 - 28 = 16 ≠ 0
∴ The given system has no solution.
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The system of linear equationsλx + 2y + 2z = 52λx + 3y +...
A system of linear equations is a set of equations where each equation is linear. It can be written in the form:
a₁x + b₁y + c₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃
where a₁, b₁, c₁, d₁, a₂, b₂, c₂, d₂, a₃, b₃, c₃, and d₃ are constants, and x, y, and z are variables.
The goal of solving a system of linear equations is to find the values of x, y, and z that satisfy all of the equations simultaneously. This can be done by using methods such as substitution, elimination, or matrix algebra.
The solution to a system of linear equations can be classified as follows:
- If there is a unique solution where x, y, and z have specific values, the system is called consistent and independent.
- If there are no solutions, the system is called inconsistent.
- If there are infinitely many solutions where x, y, and z can have any values, the system is called consistent and dependent.
Solving a system of linear equations is a fundamental concept in linear algebra and has applications in various fields such as physics, engineering, and economics.
a₁x + b₁y + c₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃
where a₁, b₁, c₁, d₁, a₂, b₂, c₂, d₂, a₃, b₃, c₃, and d₃ are constants, and x, y, and z are variables.
The goal of solving a system of linear equations is to find the values of x, y, and z that satisfy all of the equations simultaneously. This can be done by using methods such as substitution, elimination, or matrix algebra.
The solution to a system of linear equations can be classified as follows:
- If there is a unique solution where x, y, and z have specific values, the system is called consistent and independent.
- If there are no solutions, the system is called inconsistent.
- If there are infinitely many solutions where x, y, and z can have any values, the system is called consistent and dependent.
Solving a system of linear equations is a fundamental concept in linear algebra and has applications in various fields such as physics, engineering, and economics.
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The system of linear equationsλx + 2y + 2z = 52λx + 3y + 5z = 84x + λy + 6z = 10 hasa)infinitely many solutions when λ= 2b)no solution when λ= 8c)a unique solution when λ= -8d)no solution when λ= 2Correct answer is option 'D'. Can you explain this answer?
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