Q75.The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z = 0; 2x + 2y + z = 0 possess a non-zero solution is (1) 2 (2) 1 (3) zero (4) 3
What This Question Tests
The problem requires finding the values of 'k' for which a system of homogeneous linear equations has non-zero solutions. This involves setting the determinant of the coefficient matrix to zero and solving the resulting equation.
Concepts Tested
Formulas Used
For a homogeneous system Ax=0 to have a non-zero solution, det(A) must be 0
📚 NCERT Sections This Tests
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- Non-zero solution of homogeneous linear equations
- Year
- 2011
- Shift
- Unknown
- Q Number
- Q75
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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