MathematicsMedium244×since 2002Q4622Let S1_11 and S2_22 be respectively the sets of all a∈R−{0}a \in \mathbb{R} - \{ 0\}a∈R−{0} for which the system of linear equations ax+2ay−3az=1ax + 2ay - 3az = 1ax+2ay−3az=1 (2a+1)x+(2a+3)y+(a+1)z=2(2a + 1)x + (2a + 3)y + (a + 1)z = 2(2a+1)x+(2a+3)y+(a+1)z=2 (3a+5)x+(a+5)y+(a+2)z=3(3a + 5)x + (a + 5)y + (a + 2)z = 3(3a+5)x+(a+5)y+(a+2)z=3 has unique solution and infinitely many solutions. ThenAn(S1)=2\mathrm{n({S_1}) = 2}n(S1)=2 and S2_22 is an infinite setBS1=Φ\mathrm{{S_1} = \Phi}S1=Φ and S2=R−{0}\mathrm{{S_2} = \mathbb{R} - \{ 0\}}S2=R−{0}CS1=R−{0}\mathrm{{S_1} = \mathbb{R} - \{ 0\}}S1=R−{0} and S2=Φ\mathrm{{S_2} = \Phi}S2=ΦDS1_11 is an infinite set and n(S2_22) = 2Check answerSkip