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Let S be the set of all distinct values of b for which the system x + y + z = 1, x + a y + z = 1, a x + b y + z = 0 has no solution. Then S is:
- a singleton
- an empty set
- an infinite set
- a finite set with two or more elements
Correct answer: a singleton
Solution
The determinant is -(a-1)², zero only at a = 1; with a = 1 the system has no solution exactly when b = 1, so S = {1}, a singleton.
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