NCERT Class 12 · Ch 4 Exercise 4.5 · Q4
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.5 Question 4
Examine consistency: x+y+z=1, 2x+3y+2z=2, ax+ay+2az=4.
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: For a≠0: x=2−4/a, y=0, z=4/a−1, uniquely. For a=0: inconsistent.
- The coefficient determinant is a. For a≠0 the matrix is invertible.
- Subtract twice equation 1 from equation 2 to obtain y=0. Divide equation 3 by a and subtract equation 1 to get z=4/a−1.
- Equation 1 then gives x=2−4/a. Substitution verifies all three equations.
- If a=0 the third equation reads 0=4, a contradiction. There is no solution in that case.
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