JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(2 x+3 y-z=5\); \(x+\alpha y+3 z=-4\); \(3 x-y+\beta z=7\) has infinitely many solutions, then \(13 \alpha \beta\) is equal to
- A \(1110\)
- B \(1120\)
- C \(1210\)
- D \(1220\)
Answer & Solution
Correct Answer
(B) \(1120\)
Step-by-step Solution
Detailed explanation
Using family of planes \(2 \mathrm{x}+3 \mathrm{y}-\mathrm{z}-5=\mathrm{k}_1(\mathrm{x}+\alpha \mathrm{y}+3 \mathrm{z}+4)+\mathrm{k}_2(3 \mathrm{x}-\mathrm{y}+\beta \mathrm{z}-7)\)…
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