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Determinants
NCERT Class 12
CBSE
Grade 12
Question:
Find values of $a$ and $b$ such that system of equations $x + y + z = 6, x + 2y + 3z = 10, x + 2y + az = b$ has: (i) unique solution, (ii) no solution, (iii) infinitely many solutions.
Step-by-Step Solution
$|A| = a - 3$. (i) Unique solution: $a eq 3, b \in \mathbb{R}$. [1.0 Mark] (ii) No solution: $a = 3, b eq 10$. [1.0 Mark] (iii) Infinite solutions: $a = 3, b = 10$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Evaluating condition for unique solution: 1.0 Mark Evaluating condition for no solution: 1.0 Mark Evaluating condition for infinite solutions: 1.0 Mark
Correct Answer:
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