JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Consider the following system of equations : \(x+2 y-3 z=a\) ; \(2 x+6 y-11 z=b\) ; \(x-2 y+7 z=c\) where \(a , b\) and \(c\) are real constants. Then the system of equations :
- A has a unique solution when \(5 a =2 b + c\)
- B has infinite number of solutions when \(5 a =2 b + c\)
- C has no solution for all \(a , b\) and \(c\)
- D has a unique solution for all \(a , b\) and \(c\)
Answer & Solution
Correct Answer
(B) has infinite number of solutions when \(5 a =2 b + c\)
Step-by-step Solution
Detailed explanation
\(P_{1}: x+2 y-3 z=a\) \(P_{2}: 2 x+6 y-11 z=b\) \(P_{3}: x-2 y+7 z=c\) Clearly \(5 P _{1}=2 P _{2}+ P _{3} \quad\) if \(5 a =2 b + c\) \(\Rightarrow\) All the planes sharing a line of intersection \(\Rightarrow\) infinite solutions
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