JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(2x + 2y + 3z = a\) ; \(3x - y + 5z = b\) ; \(x - 3y + 2z = c\) Where \(a, b, c\) are non zero real numbers, has more than one solution, then
- A \(b \,-\, c \,+\, a = 0\)
- B \(b\, -\, c\, -\,a = 0\)
- C \(a \,+\, b\, +\, c = 0\)
- D \(b \,+ \,c\, -\,a = 0\)
Answer & Solution
Correct Answer
(B) \(b\, -\, c\, -\,a = 0\)
Step-by-step Solution
Detailed explanation
\(2x+2y+3z=a\) \((1)\) \(3x-y+5z=b\) \((2)\) \(x-3y+2z=c\) \((3)\) \((2x+2y+3z)+(x-3y+2z)-(3x-y+5z)=0\) \( \Rightarrow \) \(a+c-b=0\)
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