Q86.If the system of equations kx + y + 2z = 1 3x −y −2z = 2 −2x −2y −4z = 3 has infinitely many solutions, then k is equal to ______ .
What This Question Tests
The question tests the condition for a system of linear equations to have infinitely many solutions, specifically that the determinant of the coefficient matrix must be zero, and at least one of the augmented determinants must also be zero (or Cramer's rule condition).
Concepts Tested
Formulas Used
For infinitely many solutions, det(A)=0 and det(A_x)=det(A_y)=det(A_z)=0
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📋 Question Details
- Chapter
- Determinants
- Topic
- System of Linear Equations
- Year
- 2021
- Shift
- 25 Feb Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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