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JEE Main 2023 · 25 Jan · Shift 1

JEE Main 2023 Mathematics question on Matrices and Determinants

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=1ax + 2ay - 3az = 1

(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

has unique solution and infinitely many solutions. Then
  1. A.
    n(S1)=2n(S_1) = 2 and S2S_2 is an infinite set
  2. B.
    S1=R−{0}S_1 = \mathbb{R} - \{0\} and S2=ΦS_2 = \Phi
  3. C.
    S1S_1 is an infinite set and n(S2)=2n(S_2) = 2
  4. D.
    S1=ΦS_1 = \Phi and S2=R−{0}S_2 = \mathbb{R} - \{0\}
Show answer

Correct option: B

[JEE Main 2023 · 25 Jan · Shift 1]

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