Q70.If the system of equations ๐ฅ+ ๐ฆ+ ๐ง= 6 2๐ฅ+ 5๐ฆ+ ๐ผ๐ง= ๐ฝ ๐ฅ+ 2๐ฆ+ 3๐ง= 14 has infinitely many solutions, then ๐ผ+ ๐ฝ is equal to (1) 8 (2) 36 (3) 44 (4) 48
What This Question Tests
This question assesses the understanding of the conditions for a system of linear equations to have infinitely many solutions, requiring the determinant of the coefficient matrix and related determinants to be zero.
Concepts Tested
Formulas Used
For infinitely many solutions: det(A) = 0 and det(Aโ) = det(Aแตง) = det(Aโ) = 0 (or equivalent condition rank(A) = rank(A|B) < n)
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๐ Question Details
- Chapter
- Determinants
- Topic
- System of linear equations (infinitely many solutions)
- Year
- 2022
- Shift
- 29 Jul Shift 2
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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