Q72.If the system of equations x −2 y + 3z = 9 2x + y + z = b x −7y + az = 24, has infinitely many solutions, then a −b is equal to ______
What This Question Tests
This question requires applying the conditions for a system of three linear equations in three variables to have infinitely many solutions, which involves setting the determinant of the coefficient matrix to zero and related conditions.
Concepts Tested
Formulas Used
For a system AX=B to have infinitely many solutions, det(A)=0 and det(A_i)=0 for all i (or rank(A) = rank(A|B) < n)
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📋 Question Details
- Chapter
- Determinants
- Topic
- System of linear equations (infinitely many solutions)
- Year
- 2020
- Shift
- 04 Sep Shift 1
- Q Number
- Q72
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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