Question

Let $S_1$ and $S_2$ be respectively the sets of all $a \in R -\\{0\\}$ for which the system of linear equations $a x+2 a y-3 a z=1$ $(2 a+1) x+(2 a+3) y+(a+1) z=2$ $(3 a+5) x+(a+5) y+(a+2) z=3$ has unique solution and infinitely many solutions Then

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

Answer 1

Answer: (C)

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

Answer 2

?=||?a2a+13a+5?2a2a+3a+5?-3aa+1a+2?||?
=a(15a2+31a+36)=0?a=0
??=0�for�all�a?R-{0}
Hence S1?=R-{0}S2?=F