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Matrices and Determinants question

2023 · 25 Jan · Shift 1 · Q36

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JEE Main
Mathematics
Matrices and Determinants
2023 · 25 Jan · Shift 1 · Q36

Matrices and Determinants question

2023 · 25 Jan · Shift 1 · Q36

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let S

_1

and S

_2

be respectively the sets of all

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

has unique solution and infinitely many solutions. Then

A
$\mathrm{n({S_1}) = 2}$ and S $_2$ is an infinite set
B
$\mathrm{{S_1} = \Phi}$ and $\mathrm{{S_2} = \mathbb{R} - \{ 0\}}$
C
$\mathrm{{S_1} = \mathbb{R} - \{ 0\}}$ and $\mathrm{{S_2} = \Phi}$
D
S $_1$ is an infinite set and n(S $_2$ ) = 2

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