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Let S 1 and S 2 be respectively the sets of a   R −  0   for which the system of linear equations ax + 2 ay – 3 az = 1 (2 a + 1) x + (2 a + 3) y + ( a + 1 ) z = 2 (3 a + 5) x + ( a + 5) y + ( a + 2) z = 3 has unique solution and infinitely many solutions. Then

1. S 1 =  and S 2 = R −  0 
2. S 1 = R −  0  and S 2 = 
3. S 1 is an infinite set and n ( S 2 ) = 2
4. n ( S 1 ) = 2 and S 2 is an infinite set

Correct answer: S 1 = R −  0  and S 2 = 

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