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IIT JEE

Practice

Algebra

Theory of equations

Quick practice

Question 1 of 5

Let S_1 and S_2 be respectively the sets of all \mathrm{a} \in \mathrm{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

S_1=\mathbb{R}-\{0\} and S_2=\Phi

B

\mathrm{S}_1 is an infinite set an \mathrm{n}\left(\mathrm{S}_2\right)=2

C

S_1=\Phi and S_2=\mathbb{R}-\{0\}

D

\mathrm{n}\left(\mathrm{S}_1\right)=2 and \mathrm{S}_2

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