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 (1) $\mathrm { n } \left( S _ { 1 } \right) = 2$ and $S _ { 2 }$ is an infinite set (2) $S _ { 1 }$ is an infinite set and $n \left( S _ { 2 } \right) = 2$ (3) $S _ { 1 } = \phi$ and $S _ { 2 } = \mathbb { R } - \{ 0 \}$ (4) $S _ { 1 } = \mathbb { R } - \{ 0 \}$ and $S _ { 2 } = \phi$
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\\
(1) $\mathrm { n } \left( S _ { 1 } \right) = 2$ and $S _ { 2 }$ is an infinite set\\
(2) $S _ { 1 }$ is an infinite set and $n \left( S _ { 2 } \right) = 2$\\
(3) $S _ { 1 } = \phi$ and $S _ { 2 } = \mathbb { R } - \{ 0 \}$\\
(4) $S _ { 1 } = \mathbb { R } - \{ 0 \}$ and $S _ { 2 } = \phi$