JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(7 x+11 y+\alpha z=13\) \(5 x+4 y+7 z=\beta\) \(175 x+194 y+57 z=361\) has infinitely many solutions, then \(\alpha+\beta+2\) is equal to
- A \(4\)
- B \(3\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
Sol. \(7 x+11 y+\alpha z=13\) \(5 x+4 y+7 z=\beta\) \(175 x+194 y+57 z=361\) \(\text { (i) } \times 10+(\text { ii }) \times 21-(\text { iii) }\) \(z (10 \alpha+147-57)=130+21 \beta-361\) \(\therefore 10 \alpha+90=0\) \(\alpha=-9\) \(130-361+21 \beta=0\) \(\beta=11\)…
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