JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(x-2 y+z=-4 \); \(2 x+\alpha y+3 z=5 \); \(3 x-y+\beta z=3\) has infinitely many solutions, then \(12 \alpha+13 \beta\) is equal to
- A \(60\)
- B \(64\)
- C \(54\)
- D \(58\)
Answer & Solution
Correct Answer
(D) \(58\)
Step-by-step Solution
Detailed explanation
\(\mathrm{D}=\left|\begin{array}{ccc}1 & -2 & 1 \\ 2 & \alpha & 3 \\ 3 & -1 & \beta\end{array}\right|\) \(=1(\alpha \beta+3)+2(2 \beta-9)+1(-2-3 \alpha)\) \(=\alpha \beta+3+4 \beta-18-2-3 \alpha\) For infinite solutions \(\mathrm{D}=0, \mathrm{D}_1=0, \mathrm{D}_2=0\) and…
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