Two fair dice are thrown. The numbers on them are taken as $λ$ and $μ,$ and a system of linear equations
$x + y + z = 5$
$x + 2 y + 3 z = μ$
$x + 3 y + λ z = 1$
is constructed. If $p$ is the probability that the system has a unique solution and $q$ is the probability that the system has no solution, then:

Question

Two fair dice are thrown. The numbers on them are taken as $λ$ and $μ,$ and a system of linear equations
$x + y + z = 5$

$x + 2 y + 3 z = μ$

$x + 3 y + λ z = 1$
is constructed. If $p$ is the probability that the system has a unique solution and $q$ is the probability that the system has no solution, then:

Aicharya · Accepted Answer

1 1 1 1 2 3 1 3 &#955; = &#955; - 5 &#916; 1 = 1 1 5 2 3 &#956; 3 &#955; 1 = 10 &#955; + 3 &#956; - &#955;&#956; - 44 &#916; 2 = 1 1 5 1 3 &#956; 1 &#955; 1 = 5 &#955; + &#956; - &#955;&#956; - 13 &#916; 3 = 1 1 5 1 2 &#956; 1 3 1 = - 2 &#956; + 6 For unique solution &#955; &#8800; 5 , &#956; &#8712; { 1 , 2 , 3 , 4 , 5 , 6 } &#8658; p = 5 6 &#215; 1 = 5 6 For No Solution &#955; = 5 , &#160; &#956; &#8800; 3 &#8658; &#160;&#160; q = 1 6 &#215; 5 6 = 5 36

Two fair dice are thrown. The numbers on them are taken as &#955; and &#956; , and a system of linear…

Solution

Two fair dice are thrown. The numbers on them are taken as λ and μ , and a system of linear…