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The system x1 + 2*x2 + 3*x3 = 6, x1 + 3*x2 + 5*x3 = 9, 2*x1 + 5*x2 + a*x3 = b is consistent with infinitely many solutions. Then:

1. a in R - {8} and b in R - {15}
2. a = 8, b can be any real number
3. a = 8, b = 15
4. b = 15, a can be any real number

Correct answer: a = 8, b = 15

Solution

Adding equations 1 and 2 yields 2*x1 + 5*x2 + 8*x3 = 15, so consistency with infinite solutions requires a = 8 and b = 15.

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