JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations
\(x + 5y + 6z = 4\),
\(2x + 3y + 4z = 7\),
\(x + 6y + az = b\)
has infinitely many solutions, then the point \((a, b)\) lies on the line
- A \(y - x = 3\)
- B \(x - y = 3\)
- C \(x + y = 11\)
- D \(x + y = 12\)
Answer & Solution
Correct Answer
(B) \(x - y = 3\)
Step-by-step Solution
Detailed explanation
For the given system of equations to have infinitely many solutions, the determinant of the coefficient matrix must be zero, \(\Delta = 0\). \(\Delta = \begin{vmatrix} 1 & 5 & 6 \\ 2 & 3 & 4 \\ 1 & 6 & a \end{vmatrix} = 0\) Expanding along the first row:…
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