Q73.Let S be the set of all integer solutions (x, y, z) of the system of equations x −2 y + 5 z = 0 −2 x + 4 y + z = 0 −7 x + 14 y + 9 z = 0 such that 15 ≤x2 + y2 + z2 ≤150. Then, the number of elements in the set S is equal to ..........
What This Question Tests
This question involves solving a system of homogeneous linear equations. It requires finding the rank of the coefficient matrix or the determinant to determine the nature of solutions, and then finding integer solutions within a given bound.
Concepts Tested
Formulas Used
Determinant of coefficient matrix
Properties of homogeneous systems
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📋 Question Details
- Chapter
- Matrices
- Topic
- Homogeneous System of Linear Equations
- Year
- 2020
- Shift
- 03 Sep Shift 2
- Q Number
- Q73
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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