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MCQMediumJEE Main 2023 · 25 January, Shift 1Solving Linear Equations (Matrix Method)

Mathematics Question from JEE Main 2023 · 25 January, Shift 1

Let S1S_1 and S2S_2 be respectively the sets of all a∈R−{0}a \in \mathbb{R} - \{0\} for which the system of linear equations:

ax+2ay−3az=1,(2a+1)x+(2a+3)y+(a+1)z=2,(3a+5)x+(a+5)y+(a+2)z=3,\begin{aligned} ax + 2ay - 3az &= 1,\\ (2a + 1)x + (2a + 3)y + (a + 1)z &= 2,\\ (3a + 5)x + (a + 5)y + (a + 2)z &= 3, \end{aligned}

has unique solution and infinitely many solutions. Then:

  • A

    n(S1)=2n(S_1) = 2 and S2S_2 is an infinite set

  • B

    S1S_1 is an infinite set and n(S2)=2n(S_2) = 2

  • C

    S1=∅S_1 = \emptyset and S2=R−{0}S_2 = \mathbb{R} - \{0\}

  • D

    S1=R−{0}S_1 = \mathbb{R} - \{0\} and S2=∅S_2 = \emptyset

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